Having trouble with a pre calc problem.

Question

Ive gotten most of the way through it. its f(x)=x^(4)-2x^(3)+x^(2). Im trying to identify the zeros, and cant seem to get there. ive worked it down to (x^(2))(x^(2)-2x+1) and need to find 2 values where the two xs,(Represented by x and y for now) are x(y)=2, but at the same time, x+y=-2. help please.

Ive done a calculations online. On two different website, i get the two zeros (x and y) as either 1 and 1 or 1 and 0!?!

Answer 1

What you have here is correct. If you start off by factoring, you get:

x²(x²-2x+1) You can factor this further

x²(x-1)(x-1)=0 You set each factor equal to zero and solve:

x=0 (There are 2 of these because of the x²)

x=0

x-1=0, x=1

x-1=0, x=1

You have 4 zeros, they are 2 distinct zeros with a multiplicity of 2. You can confirm this on the graph, they touch the axis at this point but doesn't go through.