Question

Let $f\left(x\right)$ be a polynomial of degree 3 having extremum at $x=\frac{-1}{3},1$ and $f\left(2\right)=0.$

Number of distinct real roots of the equation $f\left(f\right(x\left)\right)=0,$ is

• A. 1
• B. 3
• C. 5
• D. 9

Answer 1

The correct option is A 1

$f\left(x\right)=x^3-x^2-x-2$
As $f\left(x\right)=0$ has exactly one real root i.e., $x=2.$

$\therefore f\left(f\right(x\left)\right)=0\Rightarrow f\left(x\right)=2$, which is satisfied by exactly one real $x$.