Question

If $k\sqrt{-1}$ is a root of the equation $x^4+6x^3-16x^2+24x-80=0$, then $k=$

• A. $\pm 1$
• B. $\pm 2$
• C. $\pm 3$
• D. $\pm 4$

Answer 1

The correct option is B $\pm 2$

Given, $k\sqrt{-1}$ is a root of the equation $x^4+6x^3-16x^2+24x-80=0$.

Substituting $x=ik$ in the given equation, 0 get
${\left(ik\right)}^4+6{\left(ik\right)}^3-16{\left(ik\right)}^2+24\left(ik\right)-80=0\Rightarrow k^4-i6k^3+16k^2+24ik-80=0$
And from options $k=\pm 2$ satisfies this.