Question

The cubic polynomial $p\left(a\right)=a^3-a$ has ................ zeros.

• A. $0$
• B. $1$
• C. $2$
• D. $3$

Answer 1

The correct option is D $3$

Given : $p\left(a\right)=a^3-a$

$\therefore$ $p\left(a\right)=a(a^2-1)$

$\therefore$ $p\left(a\right)=a(a^2-1)=a(a+1)(a-1)$

But, to find number of zeros of $p\left(a\right)$, we need to equate it to zero

$\therefore p\left(a\right)=0$

$\therefore$ $a(a+1)(a-1)=0$

$\therefore$ $a=0,a=-1$ and $a=1$

Hence, $p\left(a\right)$ has $3$ zeroes.