Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationMiscellaneous/MixedMedium2 minQB

MathematicsMediumsingle choice

Passage / Comprehension

Let $f (x) = x^{4} + a x^{3} + b x^{2} + a x + 1$ be a polynomial where $a$ and $b$ are real numbers.

If $f (x) = 0$ has two different pairs of equal roots, then the value of $a + b$ is

Answer:

Solution:

Let $x^{4} + ax^{3} + bx^{2} + ax + 1 = (x^{2} + kx + 1)^{2}$

comparing $2 k = a; b = k^{2} + 2 \Rightarrow a + b = (k + 1)^{2} + 1$ it can be 4

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:Miscellaneous/Mixed

⏱ 2mℹ️ Source: QB

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