The condition that the product of two of the following roots $x^{3} + p x^{2} + q x + r = 0$ may be $- 1$ is

r^{2} + p r + q + 1 = 0

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q^{2} + p q + q + 1 = 0

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p^{2} + p q + p + 1 = 0

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r^{2} - p r - q + 1 = 0

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Solution

The correct option is A $r^{2} + p r + q + 1 = 0$
product of roots $= - r$
product of two roots $= - 1$
third root $= r$
$r^{3} + {p r}^{2} + r q + r = 0 r^{2} + p r + q + 1 = 0$

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