Q53 / 155 · WBJEE 2016 · Mathematics

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

Correct answer
A
$p=1, q=-2$
B
$p=0, q=1$
C
$p=-2, q=0$
D
$p=-2, q=1$

Solution

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 $2 \times 1+q=0$ $\begin{array}{lr}\Rightarrow & q+2=0 \\ \Rightarrow & q=-2 \\ \text { Hence, } p=1, q=-2\end{array}$

Hence, the correct answer is option: 'A'.

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