# What is the condition that one root of the quadratic equation ax^2 + bx + c =0 is reciprocal of the other ?

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What is the condition that one root of the quadratic equation ax2 + bx + c=0 is reciprocal of the other ?

A) a = b

B) b = c

C) a = c

D) a + b + c = 0

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Correct option is (C) a = c

Let $\alpha\;and\;\frac1\alpha$ be roots of equation $ax^2+bx+c=0.$

$\therefore$ Product of roots $=\frac ca$

$\Rightarrow\frac ca=\alpha.\frac1\alpha=1$

$\Rightarrow$ c = a

Hence, the condition that one root of the quadratic equation $ax^2+bx+c=0$ is reciprocal of the other is a = c.

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Correct option is C) a = c