Question

If there is a root of order $3$ for the equation $x^4-2x^3+2x-1=0$, then the other root is:

• A. $-1$
• B. $0$
• C. $1$
• D. $2$

Answer 1

The correct option is A $-1$

If the order of root is $3$, $f"\left(c\right)=0$, where the $c$ is the root of order $3$.
$c=0$ or $1$.

But $0$ is not a root of the original eqn., hence $c=1$.
Find the fourth root from sum of roots
$1+1+1+d=2$
$d=-1$