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  4. If p and q are the roots of the equation x2+p x+q=0, then

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

Complex Numbers and Quadratic Equations

Solution:

$p+q=-p$ and $p q=q$
$ \Rightarrow q(p-1)=0$
$\Rightarrow q=0$ or $p=1$
If $q=0$, then $p=0$, i.e. $p=q$
$\therefore p=1$ and $q=-2$