how many x - intercepts appear on the graph of this polynomial function?\nf(x)=x^{4}-5x^{2}\n1 x…

Answer:

C. 3 x - intercepts

Explanation:

Step1: Set the function equal to 0.

$f(x)=x^{4}-5x^{2}=0$

Step2: Factor out the common factor.

$x^{2}(x^{2} - 5)=0$

Step3: Use the zero - product property.

$x^{2}=0$ or $x^{2}-5 = 0$

Step4: Solve each equation.

For $x^{2}=0$, we get $x = 0$. For $x^{2}-5=0$, we have $x^{2}=5$, so $x=\pm\sqrt{5}$. So the x - intercepts are $x = 0,x=\sqrt{5},x =-\sqrt{5}$, a total of 3 x - intercepts.