If p,q,r are positive and in A.P., the roots of px²+qx+r=0 are real for (a) | rp-7 | 4 3 (b) | pr-7 | 4 3 (c) all p and r (d) no p and r

Correct answer: (b) | pr-7 | 4 3 q= p+r 2, and q² 4pr→(p+r)² 16pr→ ( pr )²-14 pr+1 0→ | pr-7 | 4 3. JEE Advanced 1994 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

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[JEE Advanced 1994] if p q r are positive and in a p the roots of px

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If $p,q,r$ are positive and in A.P., the roots of $px^2+qx+r=0$ are real for

(a) $\left|\frac rp-7\right|\ge4\sqrt3$
(b) $\left|\frac pr-7\right|\ge4\sqrt3$
(c) all $p$ and $r$
(d) no $p$ and $r$

1 Answer

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

Correct answer: (b) $\left|\frac pr-7\right|\ge4\sqrt3$

$q=\frac{p+r}2$, and $q^2\ge4pr\Rightarrow(p+r)^2\ge16pr\Rightarrow\left(\frac pr\right)^2-14\frac pr+1\ge0\Rightarrow\left|\frac pr-7\right|\ge4\sqrt3$.

JEE Advanced 1994 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

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