If α,β are roots of x²+px+q=0 and α⁴,β⁴ are roots of x²-rx+s=0, then x²-4qx+2q²-r=0 always has (a) two real roots (b) two positive roots (c) two negative roots (d) one positive and one negative root

JEE PYQ

[JEE Advanced 1989] if alpha beta are roots of x 2 px q 0 and alpha 4

VAVidaara Admin Asked 2d ago 0 views 1 answer

If $\alpha,\beta$ are roots of $x^2+px+q=0$ and $\alpha^4,\beta^4$ are roots of $x^2-rx+s=0$, then $x^2-4qx+2q^2-r=0$ always has

(a) two real roots
(b) two positive roots
(c) two negative roots
(d) one positive and one negative root

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

Correct answer: (a) two real roots

With $r=\alpha^4+\beta^4=(p^2-2q)^2-2q^2$, the discriminant is $4(p^2-2q)^2\ge0$, so there are always two real roots.

JEE Advanced 1989 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

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