Question

Given that one root of the equation $x^3-10x^2+31x-30=0$ is $5$ then other roots are

• A. $2$ and $3$
• B. $2$ and $4$
• C. $3$ and $4$
• D. $-2$ and $-3$

Answer 1

The correct option is A $2$ and $3$

Method I:
Let $f\left(x\right)=x^3-10x^2+31x-30=0$
$\because f\left(2\right)=2^3-10(2{)}^2+31(2)-30-0$ and $f\left(3\right)=3^3-10(3{)}^2+31(3)-30=0$
So, $x=2$ & $3$ are the other roots of given equation
Method II:
$x^3-10x^2+31-30=0$
$\therefore (x-5)(x^2-5x+6)=0$
or $(x-5)(x-3)(x-2)=0$
$\therefore x=5,3,2$