Question

The number of distinct roots of the cubic polynomial equation $x^3-x^2=0$ is

• A. $3$
• B. $1$
• C. $2$

Answer 1

The correct option is C $2$

The graph of the cubic polynomial $f\left(x\right)=x^3-x^2$ is given by
We see that the graph of $f\left(x\right)$ intersects the x-axis at $2$ distinct points.
Hence $f\left(x\right)=0\text{has}2$ distinct roots.

Alternate method:
$x^3-x^2=0\Rightarrow x^2(x-1)=0$
$\Rightarrow x^2=0\text{or}x=1$
$\Rightarrow x=0\text{or}x=1$