Zeros and multiplicity of each zero for the polynomial function x^4-2x^2+1

Question

I'm in algebra two and this is in my homework. 

Answer 1

To find the zeros of a polynomial you have to find where the graph would intersect the x axis.  To do this, you have to find some way to either graph the equation, or as is better here, to factor it.

Factoring the polynomial x⁴ - 2x² + 1, you come up with:

(x² -1)(x² -1)

They are both the same so you only have to set one equal to zero to find the x intercept(s).

x² - 1 = 0

x² = 1

x = √1

x = ± 1

That means that there are 2 x intercepts, at 1 and -1, but you have 2 factors that are exactly the same, so you have a multiplicity of zeros.  So 1 has a multiplicity of 2, and -1 has a multiplicity of 2.