Let α,β be the roots of x²-px+r=0 and α2,2β the roots of x²-qx+r=0. Then r equals (a) 29(p-q)(2q-p) (b) 29(q-p)(2p-q) (c) 29(q-2p)(2q-p) (d) 29(2p-q)(2q-p)

Correct answer: (d) 29(2p-q)(2q-p) α+β=p and α2+2β=q give α= 2(2p-q) 3, β= 2q-p 3; thus r=αβ= 29(2p-q)(2q-p). JEE Advanced 2007 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

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[JEE Advanced 2007] let alpha beta be the roots of x 2 px r 0 and alpha

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Let $\alpha,\beta$ be the roots of $x^2-px+r=0$ and $\frac\alpha2,2\beta$ the roots of $x^2-qx+r=0$. Then $r$ equals

(a) $\frac29(p-q)(2q-p)$
(b) $\frac29(q-p)(2p-q)$
(c) $\frac29(q-2p)(2q-p)$
(d) $\frac29(2p-q)(2q-p)$

1 Answer

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

Correct answer: (d) $\frac29(2p-q)(2q-p)$

$\alpha+\beta=p$ and $\frac\alpha2+2\beta=q$ give $\alpha=\frac{2(2p-q)}3,\ \beta=\frac{2q-p}3$; thus $r=\alpha\beta=\frac29(2p-q)(2q-p)$.

JEE Advanced 2007 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

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