Question

One zero of the polynomial function f(x) = x3 + 9x2 + 20x is x = 0. What are the zeros of the polynomial function?

Answer 1

Given:

The function is:

`f(x)=x^3+9x^2+20x`

Find-:

What are the zeros of the polynomial function

Explanation-:

First zero at x =0 then another zero is:

`\begin{gathered} f(x)=x^3+9x^2+20x \\ \\ f(x)=0 \\ \\ x^3+9x^2+20x=0 \end{gathered}`

So, the zero is:

`\begin{gathered} x^3+9x^2+20x=0 \\ \\ x(x^2+9x+20)=0 \\ \\ x=0 \\ \\ \text{ And} \\ \\ x^2+9x+20=0 \end{gathered}`

Another zero function is:

`\begin{gathered} x^2+9x+20=0 \\ \\ x^2+5x+4x+20=0 \\ \\ x(x+5)+4(x+5)=0 \\ \\ (x+5)(x+4)=0 \\ \\ x+5=0\text{ and }x+4=0 \\ \\ x=-5\text{ and }x=-4 \end{gathered}`

The zero of a polynomial is -5 and -4