[JEE Advanced 1994] If $p,q,r$ are positive and in A.P., the roots of $px^2+qx+r=0$ are real for
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
· 1mo ago
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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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