Question

If $3$ is a zero of the polynomial $f\left(x\right)=x^4-x^3-8x^2+kx+12$, then the value of $k$ is:

• A. $-2$
• B. $2$
• C. $-3$
• D. $\frac{3}{2}$

Answer 1

The correct option is B $2$

If $3$ is a zeros of the polynomial, then $3$ must satisfy the equation $f\left(3\right)=0$.
$x^4-x^3-8x^2+kx+12=0$
$\Rightarrow 3^4-3^3-8{\left(3\right)}^2+3k+12=0$
$\Rightarrow 81-27-72+3k+12=0$
$\Rightarrow -6+3k=0$
$\Rightarrow 3k=6$
$\Rightarrow k=2$.

Therefore, option $B$ is correct.