Question

How do I find the zeros of this polynomial function? f(x)=x^3-2x^2+x

Answer 1

factor them

Answer 2

x(x^2 - 2x + 1)

= x(x-1)(x-1)

set each factor equal to zero, you get x = 0 and x = 1

Answer 3

Wouldn't that make both of them x=1 since they are both (x-1)

Answer 4

x = 0, x = 1, and x = 1 -- Yes.

Answer 5

Thanks

Answer 6

It is more often expressed with the work "multiplicity"

x = 0
x = 1 with multiplicity 2

Answer 7

So x=0 has a multiplicity of 1 and x=1 has a multiplicity of 2 since there are two "(x-1)"?

Answer 8

I think you have it. Good work.

It's not usually necessary to state the Multiplicity of 1. That is normally understood. No harm in mentioning it, though.

Answer 9

Okay, thanks!