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Determine the x intercepts of the polynomial function:

f(x)=x^4-x^2

Recall that the x intercept is a point (x,0) where our value for y is always zero. List the intercepts (x,0) from smallest to largest and separate them with a comma between each point.

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Answer:

Step-by-step explanation:

x^4 - x^2 = 0

x^2(x^2 - 1) = 0

So either x^2 = 0 or x^2 - 1 = 0

So x = 0, 0,  -1 , 1

The list is

(0, -1), (0, 0), (0, 1)

At the point (0, 0) as x^2 = 0 the graph of the function just touches (0, 0) so we write the root as x = 0, multiplicity 2.

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