Question

If the polynomial $f\left(x\right)=2x^3+m{x}^2+nx-14$ has $(x-1)$ and $(x+2)$ as its factors, find the value of $\frac{m}{n}$.

• A. $27$
• B. $\frac{1}{3}$
• C. $3$
• D. $\frac{1}{27}$

Answer 1

The correct option is C $3$

$f\left(1\right)=0\Rightarrow m+n=12$

$f(-2)=0\Rightarrow 2m-n=15$

$\Rightarrow m=9;n=3\therefore \frac{m}{n}=3$.