Question

For what value of $k$, is $-2$ a zero of the polynomial:

$f\left(x\right)=x(2-3x)+k$.

Answer 1

It is given that $-2$ is the zero of the polynomial $f\left(x\right)=x(2-3x)+k$, which means that $f(-2)=0$. Therefore, substituting $x=-2$ in the given polynomial, we have:

$f(-2)=-2[2-3(-2\left)\right]+k\Rightarrow 0=-2(2+6)+k\Rightarrow 0=(-2\times 8)+k\Rightarrow 0=-16+k\Rightarrow k=16$

Hence, $k=16$.