Question

If the equation $p{x}^2+qx+r=0$ and $r{x}^2+qx+p=0$, where $p\ne r$, have a negative common root, then value of $p-q$ is

• A. $r$
• B. $2r$
• C. $-r$
• D. None of these

Answer 1

Answer: (C)

$-r$

Let $\alpha$ be the common root
$\Rightarrow p{\alpha }^2+q\alpha +r=0$
$andr{\alpha }^2+q\alpha +p=0$
$(p-r){\alpha }^2+(r-p)=0$
$\alpha =-1$
$p-q+r=0$
$p-q=-r$