how many x-intercepts appear on the graph of this polynomial function?\n$f(x)=x^4 - 5x^2$\n\\bigcirc 1…

Answer:

3 x - intercepts

Explanation:

Step 1: Find x - intercepts

To find the x - intercepts, we set (f(x)=0), so we have the equation (x^{4}-5x^{2}=0).

Step 2: Factor the equation

Factor out (x^{2}) from the left - hand side of the equation: (x^{2}(x^{2}-5)=0).

Step 3: Solve for x

Using the zero - product property, if (ab = 0), then either (a = 0) or (b = 0). - When (x^{2}=0), we get (x = 0) (this is a repeated root, but we count it as one distinct x - intercept for now, but we will check the multiplicity later). - When (x^{2}-5=0), we can rewrite it as (x^{2}=5), and then (x=\pm\sqrt{5}).

The solutions of the equation (x^{4}-5x^{2}=0) are (x = 0), (x=\sqrt{5}), and (x =-\sqrt{5}). So there are 3 distinct x - intercepts.