Question

The value of $p$ and $q(p\ne 0,q\ne 0)$ for which $p,q$ are the roots of the equation $x^2+px+q=0$ are

Answer 1

Given: $p,q$ are the roots of the equation $x^2+px+q=0$

Now,

$\text{sum of roots}=-\frac{\text{coefficient of}x}{\text{coefficient of}{x}^2}$

$\Rightarrow p+q=-p$

$\Rightarrow q=-2p\dots \left(1\right)$

$\text{Product of roots}=\frac{\text{constant term}}{\text{coefficient of}{x}^2}$

$\Rightarrow pq=q$

$\Rightarrow p=1\dots \left(2\right)$

From $\left(1\right)$ and $\left(2\right)$, we get

$p=1,q=-2$

Option (𝐴) is correct.