Question

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

Answer 1

Answer:

The multiple zero is $x=-5$.

The multiplicity is 2

Step-by-step 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.