Question

Find the zeros of the polynomial $x^2-3x-m(m+3)$.

Answer 1

Say $f\left(x\right)=x^2-3x-m(m+3)$
By adding and subtracting $mx$, we get
$f\left(x\right)=x^2-mx-3x+mx-m(m+3)$
$=x(x-m-3)+m(x-m-3)$
$\therefore f\left(x\right)=(x-m-3)(x+m)$
Thus, $f\left(x\right)=0$
$\Rightarrow (x-m-3)(x+m)=0$
$\Rightarrow x-m-3=0,x+m=0$
$\Rightarrow x=m+3,x=-m$
Therefore, the zeros of given function $x^2-3x-m(m+3)$ are $-m$ and $m+3$.