α,β are roots of x²+2px+q=0 and α, 1β are roots of ax²+2bx+c=0 (β² -1,0,1). Statement-1: (p²-q)(b²-ac) 0. Statement-2: b≠ pa or c≠ qa. (a) S-1 True, S-2 True; S-2 correctly explains S-1 (b) S-1 True, S-2 True; S-2 NOT a correct explanation (c) S-1 True, S-2 False (d) S-1 False, S-2 True

Correct answer: (b) S-1 True, S-2 True; S-2 NOT a correct explanation Both discriminant-type quantities are perfect squares times positives, so (p²-q)(b²-ac) 0 (S-1 true); S-2 is also true but does not explain S-1. JEE Advanced 2008 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

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[JEE Advanced 2008] alpha beta are roots of x 2 2px q 0 and alpha 1 beta

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$\alpha,\beta$ are roots of $x^2+2px+q=0$ and $\alpha,\frac1\beta$ are roots of $ax^2+2bx+c=0$ ($\beta^2\notin\{-1,0,1\}$). Statement-1: $(p^2-q)(b^2-ac)\ge0$. Statement-2: $b\ne pa$ or $c\ne qa$.

(a) S-1 True, S-2 True; S-2 correctly explains S-1
(b) S-1 True, S-2 True; S-2 NOT a correct explanation
(c) S-1 True, S-2 False
(d) S-1 False, S-2 True

1 Answer

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 2d ago ▲ 0

Correct answer: (b) S-1 True, S-2 True; S-2 NOT a correct explanation

Both discriminant-type quantities are perfect squares times positives, so $(p^2-q)(b^2-ac)\ge0$ (S-1 true); S-2 is also true but does not explain S-1.

JEE Advanced 2008 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

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