Question

Write the quadratic equation whose roots are $-2$ and $-3$

Answer 1

Let $\alpha =-2$ and $\beta =-3$
$\alpha +\beta =-2-3=-5$ and $\alpha \cdot \beta =(-2)\times (-3)=6$
The required quadratic equation is
$x^2-(\alpha +\beta )x+\alpha \cdot \beta =0$
$\Rightarrow x^2-(-5)x+6=0$
$\Rightarrow x^2+5x+6=0$