If $x^2+5 a x+6=0$ and $x^2+3 a x+2=0$ have a common root then that common root is
If $x^2+5 a x+6=0$ and $x^2+3 a x+2=0$ have a common root then that common root is
3 (or) -3
2 (or) -2
2 (or) -3
-2 (or) 3
Solution
Let $y$ be a common root of $x^2+5 a x+6=0$ and $x^2+3 a x+2=0$
So, $y^2+5 a y+6=0$ and $y^2+3 a y+2=0$
$\Rightarrow 5 a y+6=3 a y+2 \Rightarrow 2 a y=-4 \Rightarrow a y=-2$
So, $y^2+5 \cdot(-2)+6=0 \Rightarrow y^2-4=0 \Rightarrow y= \pm 2$.