Question

For what value of $k$ will $3x^5+9x^4-7x^3-5x^2-4x+3k^2$ contain $x-1$ as a factor?

• A. $0$
• B. $-1$
• C. $1$
• D. Either (1) or (3)

Answer 1

The correct option is D Either (1) or (3)

$x-1$ will be the factor of $f\left(x\right)=3x^5+9x^4-7x^3-5x^2-4x+3k^2$, if
$f\left(1\right)=0$
$\Rightarrow f\left(1\right)=3(1{)}^5+9(1{)}^4-7(1{)}^3-5(1{)}^2-4\left(1\right)+3k^2=0$
$\Rightarrow 3+9-7-5-4+3k^2=0$
$\Rightarrow 3k^2=4$
$\Rightarrow k^2=\frac{4}{3}$
$\Rightarrow k=\pm \frac{2}{\sqrt{3}}$