Question

If $(x+a)$ is factor of $f\left(x\right)=x^3+a{x}^2-2x+a+4$, then $a$ is

• A. $\frac{4}{3}$
• B. $-\frac{2}{3}$
• C. $-\frac{4}{3}$
• D. $-\frac{7}{3}$

Answer 1

Answer: (C)

$-\frac{4}{3}$

Here $f\left(x\right)=x^3+a{x}^2-2x+a+4$

and $g\left(x\right)=x+a$

Here $x+a=0$

$\Rightarrow x=-a$

Put the value of $x$ in $f\left(x\right)$ function, we get

$\Rightarrow f(-a)=(-a{)}^3+a(-a{)}^2-2(-a)+a+4=0$

$\Rightarrow -a^3+a^3+2a+a=-4$

$\Rightarrow 3a=-4$

$\Rightarrow a=-\frac{4}{3}$