Question

For what value of $k$, $(-4)$ is a zero of the polynomial $x^2-x-(2k+2)$?

Answer 1

Step 1: Substitute $(-4)$ in the equation

The given equation is $x^2-x-(2k+2)$.

Substituting $x=-4$ we get,

$x^2-x-(2k+2)={\left(-4\right)}^2-\left(-4\right)-\left(2k+2\right)$

$=16+4-2k-2$

$=14-2k$

Step 2: Calculate $k$

Equating this with zero we get,

$14-2k=0$

$\Rightarrow$ $2k=14$

$\Rightarrow$ $k=\frac{14}{2}$

$\Rightarrow$ $k=7$

Hence, for $k=7$ $(-4)$ is a zero of the given polynomial.