The number of points ( p , q ) such that p , q ∈ { 1 , 2 , 3 , 4 } and the equation p x 2 + q x + 1 = 0 has real roots is

p x 2 + q x + 1 = 0 has real roots if q 2 − 4 p ≥ 0 or q 2 ≥ 4 p Since p , q ∈ { 1 , 2 , 3 , 4 } The required points(p,q) are(1,2), (1,3),(1, 4), (2,3),(2,4),(3,4),(4,4) So the required number is 7

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Mathematics - Quadratic Equation Question with Solution | TestHub

MathematicsQuadratic EquationGeneralEasy2 minQB

MathematicsEasysingle choice

The number of points ( $p, q$ ) such that $p, q \in {1, 2, 3, 4}$ and the equation $p x^{2} + q x + 1 = 0$ has real roots is

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Answer:

Solution:

$p x^{2} + q x + 1 = 0$ has real roots if $q^{2} - 4 p \geq 0$ or $q^{2} \geq 4 p$

Since $p, q \in {1, 2, 3, 4}$

The required points(p,q) are(1,2), (1,3),(1, 4), (2,3),(2,4),(3,4),(4,4)

So the required number is 7

Stream:JEESubject:MathematicsTopic:Quadratic EquationSubtopic:General

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