If $p$ and $q$ are roots of the equation $x^{2} + p x + q = 0$ , then

p = 1, q = - 2

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p = 0, q = 1

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p = - 2, q = 0

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p = - 2, q = 1

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Solution

The correct option is A $p = 1, q = - 2$
$f (x) = x^{2} + p x + q$
$f (p) = p^{2} + p^{2} + q = 0$
Hence,
$2 p^{2} = - q$ ...(i)
$p + q = - p$
$q = - 2 p$
Substituting $q$ in (1), we get
$2 p = 2 p^{2}$
Hence,
$p = 0$ or $p = 1$
If $p = 0$ then $q = 0$ or
If $p = 1$ then $q = - 2$ .

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