Question

The number of the distinct zeros of the polynomial $f\left(x\right)=x(x-4{)}^3(x-3{)}^2(x-1)$ is

• A. 4
• B. 04
• C. 4.00
• D. 4.0

Answer 1

Answer: (A), (B), (C), (D)

Given polynomial $f\left(x\right)=x(x-4{)}^3(x-3{)}^2(x-1)$
For zeros of a polynomial
$f\left(x\right)=0\Rightarrow x(x-4{)}^3(x-3{)}^2(x-1)=0\Rightarrow x=0,(x-4{)}^3=0,(x-3{)}^2=0,(x-1)=0\Rightarrow x=0,4,4,4,3,3,1$
$\therefore$ The distinct zeros of the polynomial are $x=0,1,3,4$
Hence, the number of distinct zeros of the polynomial is $4$.