Question

What is the multiple zero and multiplicity of `f(x) = x^3+10x^2+25x`?

Answer 1

zeros are `x=0 , x= 5 , x=5` and multiplicity of `x=-5` is `2`

Explanation:

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

`f(x) = x(x+5)^2 or f(x) = x(x+5)(x+5)`;

`f(x)=0` when `x=0 ; x+5=0 :. x = -5 , x = -5`

So zeros are `x=0 , x= 5 , x=5` and

Multiplicity of `x=-5` is `2` [Ans]