Question

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.Answer:

Answer 1

To find such x intercepts, we make our y-value 0 and solve for x as following:

$\begin{gathered} f(x)=x^4-x^2 \\ \rightarrow x^4-x^2=0 \\ \rightarrow(x^2)(x^2-1)=0 \\ \rightarrow(x^2)(x+1)(x-1)=0 \\ \\ x^2=0\rightarrow x_1=0 \\ \\ x+1=0\rightarrow x_2=-1 \\ \\ x-1=0\rightarrow x_3=1 \end{gathered}$

This way, we can conclude that the x intercepts are:

-1,0,1