Question

What is the multiple zero and multiplicity of f(x) = x3 + 10x2 + 25x?

Answer 1

The multiple zero is
`x=-5`.

The multiplicity is 2

Explanation:

The given function is

`f(x)=x^3+10x^2+25x`

To find the zero of this function, we equate it to zero.

`\Rightarrow x^3+10x^2+25x=0`

We factor to obtain;

`x(x^2+10x+25)=0`

Observe that; the expression within the parenthesis is a perfect square.

This implies that;

`x(x+5)^2=0`

This implies that;

Either
`x=0` or
`(x+5)^2=0`

`(x+5)^2=0` has a multiple zero which is

`x=-5` and its multplicity is 2.