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If $p, q$ are the roots of the equation $x^{2}+p x+q=0,$ then
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Verified Answer
The correct answer is:
$p=1, q=-2$
Given, $\rho, q$ are roots of equation $x^{2}+p x+q=0$
$\therefore \quad p+q=-p \Rightarrow 2 p+q=0$
$\begin{array}{lr}\text { and } & p q=q \\ \Rightarrow & \rho=1\end{array}$
Put $p=1$ in Eq, we get $2 \times 1+q=0$
$\begin{array}{lr}\Rightarrow & q+2=0 \\ \Rightarrow & q=-2 \\ \text { Hence, } p=1, q=-2\end{array}$
$\therefore \quad p+q=-p \Rightarrow 2 p+q=0$
$\begin{array}{lr}\text { and } & p q=q \\ \Rightarrow & \rho=1\end{array}$
Put $p=1$ in Eq, we get $2 \times 1+q=0$
$\begin{array}{lr}\Rightarrow & q+2=0 \\ \Rightarrow & q=-2 \\ \text { Hence, } p=1, q=-2\end{array}$
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