Question

The sum of possible real values of $b$ for which the equations $2017x^2+bx+7102=0$ and $7102x^2+bx+2017=0$ have a common root, is

Answer 1

Let the common root be $\alpha$
$\Rightarrow 2017{\alpha }^2+b\alpha +7102=0\cdots \left(1\right)$
and $7102{\alpha }^2+b\alpha +2017=0\cdots \left(2\right)$
Subtracting $\left(2\right)$ from $\left(1\right),$ we get
$-5085{\alpha }^2+5085=0$
$\Rightarrow {\alpha }^2=1$
$\Rightarrow \alpha =\pm 1$
If $\alpha =+1,$ $b=-9119$
If $\alpha =-1,$ $b=9119$
$\therefore$ Sum of all possible values of $b$ is $0$.