If $2 x^2+3 x-2=0$ and $3 x^2+a x-2=0$ have one common root then the sum of all possible values of $a$ is
If $2 x^2+3 x-2=0$ and $3 x^2+a x-2=0$ have one common root then the sum of all possible values of $a$ is
$-3.5$
$7.5$
$-7.5$
$-1.5$
Solution
$2 x^2+3 x-2=0 \quad \Rightarrow x=-2, \frac{1}{2}$
If $x=-2$ is the common root with $3 x^2+a x-2=0$
then $3(-2)^2+a(-2)-2=0 \Rightarrow a=5$
If $x=\frac{1}{2}$ is the common root with $3 x^2+a x-2=0$
then $3\left(\frac{1}{2}\right)^2+\frac{a}{2}-2=0 \Rightarrow a=2.5$
So, sum of all possible values of $a=7.5$