Question

The roots of the equation $x^3-3x^2-6x+8=0$ are in arithmetic progression, then the roots of the equation are

• A. $3,4,5$
• B. $4,7,10$
• C. $-2,1,4$
• D. $1,4,7$

Answer 1

The correct option is C

$-2,1,4$

Explanation for the correct option

Given, $x^3-3x^2-6x+8=0$

As we know the sum of the roots of cubic polynomial of the form $a{x}^3+b{x}^2+cx+d$ is $-\frac{b}{a}$.

Here, $a=1$ and $b=-3$. Thus,

Sum of roots$=-\frac{b}{a}=-\left(\frac{-3}{1}\right)=3$.

$-2,1,4$ satisfies this condition out of all the options.

Hence the correct option is option C.