Question

The set of zeros of the cubic polynomial $f\left(x\right)=x^3-2x^2+x$ is

• A. $\{0,1,3\}$
• B. $\{0,1,2\}$
• C. $\{0,1\}$

Answer 1

The correct option is C $\{0,1\}$

Given: $f\left(x\right)=x^3-2x^2+x$

We see that $x$ is common in all the terms of the polynomial, hence we can write $f\left(x\right)$ as
$f\left(x\right)=x(x^2-2x+1)$
$\Rightarrow f\left(x\right)=x(x-1{)}^2$
Hence theset of zeros of $f\left(x\right)$ are $\{0,1,1\}\text{or}\{0,1\}$