If one root of the equation $p x^{2} + q x + r = 0$ is the reciprocal of the other, then

r = p

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p = q

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q = r

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none of these

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Solution

The correct option is A $r = p$
Let one root be m $\Rightarrow$ other roots is $\frac{1}{m}$

$∴$ product of roots $= \frac{m \times 1}{m} = 1$

$∴ \frac{r}{p} = 1$

$\Rightarrow r = p$

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If one root of the equation px2+qx+r=0 is the reciprocal of the other, then

The correct option is A r=pLet one root be m⇒ other roots is 1m∴product of roots =m×1m=1∴rp=1⇒r=p

If one root of the equation $p x^{2} + q x + r = 0$ is the reciprocal of the other, then

The correct option is A $r = p$
Let one root be m $\Rightarrow$ other roots is $\frac{1}{m}$

$∴$ product of roots $= \frac{m \times 1}{m} = 1$

$∴ \frac{r}{p} = 1$

$\Rightarrow r = p$