Question

If the roots of palynomial $P\left(x\right)=x^3-3x^2+kx+4$ are in $AP,$ then $\left|k\right|$. Has the value equal to

• A. 0
• B. 1
• C. 2
• D. 3

Answer 1

The correct option is C 2

Given roots of the polynomial are in AP

let the roots of the polynomial be $a-d,a,a+d$

$a-d+a+a+d=-\frac{-3}{1}\Rightarrow 3a=3\Rightarrow a=1$

so, $a=1$ is one of the roots of the equation

$p\left(1\right)=1^3-3\times 1^2+k+4=0\Rightarrow k+2=0\Rightarrow k=-2$

$\left|k\right|=2$