Question

The sum of roots of the polynomial equation $(x-1)(x-2)(x-3)=2(x-2)(x-3)$ is

• A. $5$
• B. $3$
• C. $1$
• D. $8$

Answer 1

The correct option is D

$8$

$(x-1)(x-2)(x-3)=2(x-2)(x-3)$
$\Rightarrow (x-1)(x-2)(x-3)-2(x-2)(x-3)=0$
$\Rightarrow (x-2)(x-3)(x-1-2)=0$
$\Rightarrow (x-2)(x-3)(x-3)=0$
Therefore, the given equation can be modified as $(x-2)(x-3{)}^2=0$, then the roots of equation are 2,3 and 3.
Hence, the sum of roots is 8.