Question

If one factor of the expression $x^3+7k{x}^2-4kx+12$ is $(x+3)$, then the value of $k$ is

• A. $5$
• B. $\frac{1}{5}$
• C. $-\frac{13}{17}$
• D. $-\frac{17}{13}$

Answer 1

The correct option is B $\frac{1}{5}$

$(x+3)$ is the factor of $f\left(x\right)=x^3+7k{x}^2-4kx+12$
Thus,$f(-3)$ must be equal to zero
$=>f(-3)=0$
$=>(-3{)}^3+7k(-3{)}^2-4k(-3)+12=0$
$=>-27+63k+12k+12=0$
$=>75k=15$
$=>k=\frac{15}{75}=\frac{1}{5}$