Mathematics › Quadratic Equation
Quadratic Equation Questions
328 questions across 9 subtopics — with step-by-step solutions.
Common Roots(18)
- Difference between the corresponding roots... | Mathematics | TestHub
- The quadratic equations and have one root... | Mathematics | TestHub
- is divisible by | Mathematics | TestHub
- The value of for which the equations have... | Mathematics | TestHub
- If the equationsandhave a common root, the... | Mathematics | TestHub
- If equationsandhave a common root, thenequ... | Mathematics | TestHub
- If three distinct numbersare in G.P. and t... | Mathematics | TestHub
- Ifandare three consecutive terms of a non-... | Mathematics | TestHub
- Letbe such that the equation,has a repeate... | Mathematics | TestHub
- Letbe in. Ifandare the roots of the equati... | Mathematics | TestHub
- Letbe such that the equationhas repeated r... | Mathematics | TestHub
- Letbe a quadratic polynomial with leading... | Mathematics | TestHub
- If for some, all have positive sign, one o... | Mathematics | TestHub
- If the value of real numberfor whichandhav... | Mathematics | TestHub
- If the equation has equal roots, where and... | Mathematics | TestHub
- If \mathrm{f}(\mathrm{x})=\frac{\mathrm{ax... | Mathematics | TestHub
- If \alpha, \beta be the roots of x^{2}+p x... | Mathematics | TestHub
- If the equations x^{3}-5 x^{2}+7 x-a=0 and... | Mathematics | TestHub
General(14)
- Let and be the roots of , and and be the r... | Mathematics | TestHub
- The product of all the rational roots of t... | Mathematics | TestHub
- Let and be the distinct roots of . If m an... | Mathematics | TestHub
- Consider the equation , where is a natural... | Mathematics | TestHub
- If the set of all , for which the equation... | Mathematics | TestHub
- The number of real roots of the equation is : | Mathematics | TestHub
- Let . If , and , then the quadratic equati... | Mathematics | TestHub
- If x^{2}+2 a x+10-3 a>0 for each x \in R ,... | Mathematics | TestHub
- The range of values of ' a ' for which all... | Mathematics | TestHub
- The value of a for which one root of the q... | Mathematics | TestHub
- The sum of all real value of k for which t... | Mathematics | TestHub
- If \alpha, \beta are the real roots of x^{... | Mathematics | TestHub
- The number of points ( \mathrm{p}, \mathrm... | Mathematics | TestHub
- If (1+K) \tan ^{2} x-4 \tan x-1+K=0 has re... | Mathematics | TestHub
Graph and Sign of Quadratic(7)
- Which of the following functions is differ... | Mathematics | TestHub
- The sum of all the real values ofSatisfyin... | Mathematics | TestHub
- The number of integral values offor which... | Mathematics | TestHub
- The probability of selecting integerssuch... | Mathematics | TestHub
- The integerfor which the inequalityis vali... | Mathematics | TestHub
- Letbe the set of positive integral values... | Mathematics | TestHub
- The quadratic expression a x^{2}+|2 a-3| x... | Mathematics | TestHub
Inequation(20)
- If are distinct real numbers and then is | Mathematics | TestHub
- Statement - 1: For every natural number .... | Mathematics | TestHub
- Match the Statements/Expressions in Column... | Mathematics | TestHub
- Let and be two natural numbers such that a... | Mathematics | TestHub
- The set of all real satisfying the inequal... | Mathematics | TestHub
- If x satisfies , then | Mathematics | TestHub
- The least integral value of such that , sa... | Mathematics | TestHub
- Let. Then: | Mathematics | TestHub
- If and are real numbers, the is always | Mathematics | TestHub
- Ifandthen | Mathematics | TestHub
- Ifandis the set of all integers, then the... | Mathematics | TestHub
- Letand. Then the number of elements inis | Mathematics | TestHub
- Letand. Then which one the following state... | Mathematics | TestHub
- The number of integral solutionofis | Mathematics | TestHub
- The solution set of is | Mathematics | TestHub
- The number of integral values of k for whi... | Mathematics | TestHub
- (L-3)Find the least integral value of a su... | Mathematics | TestHub
- The least integral value of ' a ' such tha... | Mathematics | TestHub
- If x, y, z>0 and x(1-y)>\frac{1}{4}, y(1-z... | Mathematics | TestHub
- (L-3)Let \mathrm{f}(\mathrm{x})=30-2 \math... | Mathematics | TestHub
Location of roots(17)
- If then the quadratic equation has | Mathematics | TestHub
- If both the roots of the quadratic equatio... | Mathematics | TestHub
- All the values of for which both roots of... | Mathematics | TestHub
- If the difference between the roots of the... | Mathematics | TestHub
- Consider a quadratic equation , where and... | Mathematics | TestHub
- The real numberfor which the equation,has... | Mathematics | TestHub
- If both the roots of the quadratic equatio... | Mathematics | TestHub
- Consider the quadratic equationLetbe the s... | Mathematics | TestHub
- Letbe a quadratic polynomial such that. If... | Mathematics | TestHub
- The set of all real values offor which the... | Mathematics | TestHub
- The number of integral values of, for whic... | Mathematics | TestHub
- The number of distinct real roots of the e... | Mathematics | TestHub
- Roots of the equation are | Mathematics | TestHub
- The equation 2^{2 \mathrm{x}}+(\mathrm{a}-... | Mathematics | TestHub
- Match the statements of Column I with valu... | Mathematics | TestHub
- The solution set of the inequality \left(\... | Mathematics | TestHub
- If \alpha, \beta are the roots of x^{2}-3... | Mathematics | TestHub
Maximum & minimum values(7)
- If and are distinct real numbers such that... | Mathematics | TestHub
- Letbe a quadratic polynomial such thatIfle... | Mathematics | TestHub
- The value ofsuch that sum of the squares o... | Mathematics | TestHub
- Ifthenandrespectively lie in the intervals | Mathematics | TestHub
- The minimum value of the sum of the square... | Mathematics | TestHub
- The range of the function is | Mathematics | TestHub
- If one root of x^{2}-4 a x+a+f(a)=0 is thr... | Mathematics | TestHub
Miscellaneous/Mixed(33)
- The value of | Mathematics | TestHub
- If the roots of the equation \mathrm{x}^{3... | Mathematics | TestHub
- At least one positive solutions if | Mathematics | TestHub
- If , then the number of ordered pairs sati... | Mathematics | TestHub
- Sum of all roots of the equation \underbra... | Mathematics | TestHub
- If \mathrm{f}(\mathrm{x})=0 has two differ... | Mathematics | TestHub
- If 9^{x+1}+\left(a^{2}-4 a-2\right) 3^{x}+... | Mathematics | TestHub
- If (\sqrt{(49+20 \sqrt{6})})^{\sqrt{a \sqr... | Mathematics | TestHub
- Number of positive integer n for which n^{... | Mathematics | TestHub
- For a twice differentiable function f(x),... | Mathematics | TestHub
- The value of a+b+c is | Mathematics | TestHub
- The sum of squares of all integral values... | Mathematics | TestHub
- If all the roots are imaginary and b=-1 th... | Mathematics | TestHub
- If \alpha, \beta are the roots of the equa... | Mathematics | TestHub
- The least positive integer x such that the... | Mathematics | TestHub
- (1+\mathrm{x})\left(1+\mathrm{x}+\mathrm{x... | Mathematics | TestHub
- At least one solution in (1,2) if | Mathematics | TestHub
- If \alpha, \beta are the roots of the equa... | Mathematics | TestHub
- The remainder when 2+[1!+2(2!)+3(3!)+\ldot... | Mathematics | TestHub
- If \alpha, \beta are the roots of the equa... | Mathematics | TestHub
- Match the following: Column – IColumn – II... | Mathematics | TestHub
- Let \mathrm{x}, \mathrm{y}, \mathrm{z} be... | Mathematics | TestHub
- The cubic equation whose roots are a^{-1},... | Mathematics | TestHub
- If \alpha, \beta, \gamma are the roots of... | Mathematics | TestHub
- If \alpha, \beta are the roots of the equa... | Mathematics | TestHub
- At least one negative solution if | Mathematics | TestHub
- The number of solution of the equation e^{... | Mathematics | TestHub
- Let \alpha, \beta be the roots of x^{2}-x+... | Mathematics | TestHub
- If the roots of 10 x^{3}-c x^{2}-54 x-27=0... | Mathematics | TestHub
- If \mathrm{f}(\mathrm{x})=0 has two differ... | Mathematics | TestHub
- The value of a^{-10} b^{-12} c^{-12}+a^{-1... | Mathematics | TestHub
- If \alpha, \beta are the roots of the equa... | Mathematics | TestHub
- If a, b, c are three distinct real numbers... | Mathematics | TestHub
Quadratic expression(7)
- The number of values of ' a ' for which th... | Mathematics | TestHub
- The sum of all the real roots of the equat... | Mathematics | TestHub
- If \lambda is the minimum value of the exp... | Mathematics | TestHub
- Let b and c be real numbers and define the... | Mathematics | TestHub
- The integral part of positive value of a f... | Mathematics | TestHub
- If roots x_{1} and x_{2} of x^{2}+1=x / a... | Mathematics | TestHub
- Largest integral value of m for which the... | Mathematics | TestHub
Theory of equations(205)
- If and are the roots of the equation , then | Mathematics | TestHub
- If but and then the equation having and as... | Mathematics | TestHub
- Product of real roots of the equation | Mathematics | TestHub
- If the sum of the roots of the quadratic e... | Mathematics | TestHub
- The value of ' ' for which one root of the... | Mathematics | TestHub
- The number of real solutions of the equati... | Mathematics | TestHub
- If is a root of quadratic equation , then... | Mathematics | TestHub
- If one root of the equation is 4 , while t... | Mathematics | TestHub
- Let two numbers have arithmetic mean 9 and... | Mathematics | TestHub
- The value of for which the sum of the squa... | Mathematics | TestHub
- If roots of the equation be two consectuti... | Mathematics | TestHub
- If have roots and and have roots and , the... | Mathematics | TestHub
- If the roots of the quadratic equation are... | Mathematics | TestHub
- Let be the roots of the equation and be th... | Mathematics | TestHub
- Let be real numbers. Suppose, are the root... | Mathematics | TestHub
- If the expression and must have a common f... | Mathematics | TestHub
- The smallest value of , for which both the... | Mathematics | TestHub
- If the roots of the equation be imaginary,... | Mathematics | TestHub
- If and are the roots of the equation , then | Mathematics | TestHub
- Let and be real numbers such that and . If... | Mathematics | TestHub
- If are the roots of the equation , then th... | Mathematics | TestHub
- Let and be the roots of with . If for , th... | Mathematics | TestHub
- The value of for which the equation has bo... | Mathematics | TestHub
- If the sum of the square of the roots of t... | Mathematics | TestHub
- If and 1 is a root of equation , then the... | Mathematics | TestHub
- Let and . If the quadratic equation has tw... | Mathematics | TestHub
- If and are non-zero real numbers and , the... | Mathematics | TestHub
- The values of ' ' for which one root of th... | Mathematics | TestHub
- If and are roots of the equation , such th... | Mathematics | TestHub
- If and are roots of the equation, for some... | Mathematics | TestHub
- The quadratic equationwith real coefficien... | Mathematics | TestHub
- Ifand the equation(wheredenotes the greate... | Mathematics | TestHub
- Ifare the roots of the equation, then the... | Mathematics | TestHub
- Letbe the roots of equation,. Ifare in A.P... | Mathematics | TestHub
- The sum of the roots of the equation, , is: | Mathematics | TestHub
- The equation, whereis real, has | Mathematics | TestHub
- Let S be the set of all non - zero real nu... | Mathematics | TestHub
- If the two roots of the equation,are real... | Mathematics | TestHub
- If a and bare non-zero roots of then the l... | Mathematics | TestHub
- Letandbe the roots of equation. Ifthen the... | Mathematics | TestHub
- Ifis a solution of the equation, thenis eq... | Mathematics | TestHub
- The sum of all real values ofsatisfying th... | Mathematics | TestHub
- Let. Supposeandare the roots of the equati... | Mathematics | TestHub
- If the equationsandhave a common root diff... | Mathematics | TestHub
- If are the roots of the equations then wha... | Mathematics | TestHub
- If and are real numbers then the roots of... | Mathematics | TestHub
- For the equation, if one of the roots is s... | Mathematics | TestHub
- Paragraph: Let be integers and let be the... | Mathematics | TestHub
- Paragraph: Let be integers and let be the... | Mathematics | TestHub
- If, for a positive integer, the quadratic... | Mathematics | TestHub
- If an angleof asatisfies, then the roots o... | Mathematics | TestHub
- Ifandare the roots of the quadratic equati... | Mathematics | TestHub
- If is such that the sum of the cubes of th... | Mathematics | TestHub
- Letandbe real numbers, such that the roots... | Mathematics | TestHub
- Ifis such that the sum of the cubes of the... | Mathematics | TestHub
- If one real root of the quadratic equation... | Mathematics | TestHub
- If, then length of interval in whichlies is | Mathematics | TestHub
- Ifandare the roots of the quadratic equati... | Mathematics | TestHub
- Letandbe the roots ofwithFor all positive... | Mathematics | TestHub
- The number of integral values offor which... | Mathematics | TestHub
- The number of all possible positive integr... | Mathematics | TestHub
- Ifandare the roots of the equationthenis e... | Mathematics | TestHub
- LetIfis a root of the quadratic equationthen | Mathematics | TestHub
- Letandbe roots of the equationand letandbe... | Mathematics | TestHub
- The number of real roots of the equationis : | Mathematics | TestHub
- Ifis chosen in the quadratic equationsuch... | Mathematics | TestHub
- Ifbe the ratio of the roots of the quadrat... | Mathematics | TestHub
- Let and be the roots of the quadratic equa... | Mathematics | TestHub
- The sum of the solutions of the equationis... | Mathematics | TestHub
- Letandbe the roots of the equationthenis e... | Mathematics | TestHub
- In the real number system, the equationhas | Mathematics | TestHub
- The number of real roots of the equation,is: | Mathematics | TestHub
- Ifandare the roots of the equationandandar... | Mathematics | TestHub
- The number of real solutions of the equati... | Mathematics | TestHub
- Ifandare the roots of the equation, thenis... | Mathematics | TestHub
- Ifandbe two roots of the equationThen the... | Mathematics | TestHub
- The product of the roots of the equationis : | Mathematics | TestHub
- Letandbe the roots ofandandbe the roots of... | Mathematics | TestHub
- Ifandare the roots of the equation,then th... | Mathematics | TestHub
- Let, be the set of all real roots of the e... | Mathematics | TestHub
- The least positive value of ‘’ for which t... | Mathematics | TestHub
- Consider the two sets:both the roots ofare... | Mathematics | TestHub
- Letdenote the greatest integer. Then the e... | Mathematics | TestHub
- Letandbe the roots of the equation,. Ifthen | Mathematics | TestHub
- Supposedenote the distinct real roots of t... | Mathematics | TestHub
- Letandbe two real roots of the equationwhe... | Mathematics | TestHub
- Letandbe the roots of the equation. Ifthen... | Mathematics | TestHub
- The value ofis: | Mathematics | TestHub
- The set of all values of, for which the eq... | Mathematics | TestHub
- The number of the real roots of the equati... | Mathematics | TestHub
- The sum of all integral values offor which... | Mathematics | TestHub
- Let be in If and are the roots of the equa... | Mathematics | TestHub
- The number of real solutions of the equati... | Mathematics | TestHub
- The number of pairsof real numbers, such t... | Mathematics | TestHub
- The number of real roots of the equationis... | Mathematics | TestHub
- LetandIfis a quadratic equation whose root... | Mathematics | TestHub
- Letbe two roots of the equation. Thenis eq... | Mathematics | TestHub
- Ifare roots of the equationandfor each pos... | Mathematics | TestHub
- The sum ofpower of the roots of the equati... | Mathematics | TestHub
- The number of solutions of the equationis : | Mathematics | TestHub
- Letandbe two positive numbers such thatand... | Mathematics | TestHub
- Ifandthen the value ofis equal to: | Mathematics | TestHub
- For, the number of real roots of the equat... | Mathematics | TestHub
- Letandbe two real numbers such thatand. Le... | Mathematics | TestHub
- Ifare such that(here) is a root of, thenis... | Mathematics | TestHub
- Find the value of such that the sum of the... | Mathematics | TestHub
- The value ofis equal to | Mathematics | TestHub
- Letandbe the roots of. Iffor, then the val... | Mathematics | TestHub
- Ifandare the distinct roots of the equatio... | Mathematics | TestHub
- If be a root of the equation , then the ot... | Mathematics | TestHub
- Letbe the roots of the equationandbe the r... | Mathematics | TestHub
- Letbe two non-zero real numbers. Ifandare... | Mathematics | TestHub
- The sum of all real roots of equationis | Mathematics | TestHub
- Letbe a root of the equation. Then the val... | Mathematics | TestHub
- The sum of all real values offor whichis e... | Mathematics | TestHub
- Letbe the roots of the quadratic equation.... | Mathematics | TestHub
- Let be the solutions of and be the solutio... | Mathematics | TestHub
- Ifare the roots of the equationthen the eq... | Mathematics | TestHub
- Ifandare real number such that, then the v... | Mathematics | TestHub
- For a natural number, let. Then, the value... | Mathematics | TestHub
- The sum of the cubes of all the roots of t... | Mathematics | TestHub
- Letbe the roots of the equationandbe the r... | Mathematics | TestHub
- Letbe a quadratic polynomial such that. If... | Mathematics | TestHub
- If the sum of the squares of the reciproca... | Mathematics | TestHub
- The number of real solutions of the equati... | Mathematics | TestHub
- Letandbe the numbers of real roots of the... | Mathematics | TestHub
- The number of real roots of the equation, is: | Mathematics | TestHub
- Letbe the roots of the equationand.Then,is... | Mathematics | TestHub
- Ifandare the roots of the equation, then t... | Mathematics | TestHub
- The number of points, where the curvecuts-... | Mathematics | TestHub
- Letand let the equationbe. Then the larges... | Mathematics | TestHub
- The roots of the given equation are : | Mathematics | TestHub
- Letbe a real number. Letbe the roots of th... | Mathematics | TestHub
- Let be the roots of the quadratic equation... | Mathematics | TestHub
- Let. Thenis equal to | Mathematics | TestHub
- The equationhas : | Mathematics | TestHub
- Solution of is | Mathematics | TestHub
- Letbe the three roots of the equationifthe... | Mathematics | TestHub
- The number of real roots of the equation, is | Mathematics | TestHub
- If one root of the equation is 4, while th... | Mathematics | TestHub
- Letand letbe the roots of the equation. If... | Mathematics | TestHub
- The number of real solutions of the equati... | Mathematics | TestHub
- Letbe the roots of the equationThenis equa... | Mathematics | TestHub
- LetThen the maximum value offor which the... | Mathematics | TestHub
- Solve | Mathematics | TestHub
- The roots of the given equation are : | Mathematics | TestHub
- Let be the roots of the equation . The qua... | Mathematics | TestHub
- If 2 and 6 are the roots of the equation ,... | Mathematics | TestHub
- Ifare the roots of the equation,and, then | Mathematics | TestHub
- Let be a polynomial with real coefficients... | Mathematics | TestHub
- Letbe the length of three sides of a trian... | Mathematics | TestHub
- Let the set. Thenis equal to _______. | Mathematics | TestHub
- Let be the solution of the equation and .... | Mathematics | TestHub
- Rational roots of the equation are | Mathematics | TestHub
- The number of solutions, of the equationis | Mathematics | TestHub
- The number of real solutions of the equati... | Mathematics | TestHub
- Let be roots of . If , then is equal to______ | Mathematics | TestHub
- Let be the distinct roots of the equation... | Mathematics | TestHub
- For , let and be one of its root. Then, am... | Mathematics | TestHub
- If and are the roots of the equation , then | Mathematics | TestHub
- Letandbe the roots of the equation, where.... | Mathematics | TestHub
- Let. Then the number of elements inis: | Mathematics | TestHub
- The number of real solutions of the equati... | Mathematics | TestHub
- Let , be the roots of the equation . Let .... | Mathematics | TestHub
- The sum of all the solutions of the equati... | Mathematics | TestHub
- The number of real roots of the equation is : | Mathematics | TestHub
- If the set of all , for which the roots of... | Mathematics | TestHub
- Let the set of all values of , for which b... | Mathematics | TestHub
- The sum of the squares of the roots of and... | Mathematics | TestHub
- Let and be the distinct roots of . If m an... | Mathematics | TestHub
- If the set of all , for which the equation... | Mathematics | TestHub
- Let . If , and , then the quadratic equati... | Mathematics | TestHub
- Let and be the roots of , and and be the r... | Mathematics | TestHub
- The number of solutions of the equation is: | Mathematics | TestHub
- Consider the equation , where is a natural... | Mathematics | TestHub
- The product of all the rational roots of t... | Mathematics | TestHub
- The sum, of the squares of all the roots o... | Mathematics | TestHub
- If are the roots of the equation , then th... | Mathematics | TestHub
- If \alpha, \beta are the roots of the equa... | Mathematics | TestHub
- Let and be the roots of , with . If for ,... | Mathematics | TestHub
- Let and be the roots of , with . If for ,... | Mathematics | TestHub
- If \alpha, \beta be the roots x^{2}+p x-q=... | Mathematics | TestHub
- If the equation a x^{2}-b x+12=0 where a a... | Mathematics | TestHub
- If \mathrm{a}, \mathrm{b} \in \mathrm{R} a... | Mathematics | TestHub
- The set of real parameter ' a ' for which... | Mathematics | TestHub
- Let be roots of equation , where . If assu... | Mathematics | TestHub
- If the roots of the equation x^{3}-a x^{2}... | Mathematics | TestHub
- Let P(x)=x^{2}+b x+c , where b and c are i... | Mathematics | TestHub
- Number of real roots of 2 x^{99}+3 x^{98}+... | Mathematics | TestHub
- For , let and be the roots of the equation... | Mathematics | TestHub
- The sum of all the roots of the equation is | Mathematics | TestHub
- Let and be the roots of , with . If for ,... | Mathematics | TestHub
- If \alpha, \beta be the roots x^{2}+p x-q=... | Mathematics | TestHub
- Let be real numbers. Suppose, are the root... | Mathematics | TestHub
- The number of real solutions of the system... | Mathematics | TestHub
- Let \mathrm{p}(\mathrm{x})=\mathrm{x}^{5}+... | Mathematics | TestHub
- The number of the distinct real roots of t... | Mathematics | TestHub
- Let \alpha, \beta and \gamma be the roots... | Mathematics | TestHub
- If the equation \mathrm{x}^{4}+\mathrm{px}... | Mathematics | TestHub
- The equation 2\left(\log _{3} x\right)^{2}... | Mathematics | TestHub
- Let a, b, c be the the roots of the equati... | Mathematics | TestHub
- If product of two roots of the equation x^... | Mathematics | TestHub
- A polynomial equation is said to be a reci... | Mathematics | TestHub
- For, the number of real roots of the equat... | Mathematics | TestHub
- f(x) is a polynomial of 6^{\text {th }} de... | Mathematics | TestHub
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