Question

The number of real zeroes of polynomial $P\left(x\right)=x^3-x$ is ..............

• A. 2
• B. 1
• C. 0
• D. 3

Answer 1

The correct option is D 3

Given $P\left(x\right)=x^3-x$

To find the zeros of $P\left(x\right)$, let $P\left(x\right)=0$

$⟹x^3-x=0$

$⟹x(x^2-1)=0$

$⟹x(x-1)(x+1)=0$

$⟹x=0$ and $x-1=0$ and $x+1=0$

$⟹x=0,1,-1$ are the zeros of $P\left(x\right)$

Thus, the number of zeros of $P\left(x\right)$ is $3$.

Hence, the answer is $3$.