If the sum of two of the roots of $x^{3} + p x^{2} + q x + r = 0$ is zero, then $p q =$

- r

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2 r

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- 2 r

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r

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Solution

The correct option is D $r$
Let $α, β$ and $γ$ be the roots of the equation $x^{3} + p x^{2} + q x + r = 0$
Given that, $α + β = 0$
We have $α + β + γ = - p$
Thus $γ = - p$
Substituting $γ = - p$ in the given equation,
$\Rightarrow - p^{3} + p^{3} - p q + r = 0$
$\Rightarrow p q = r$

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