How many x-incercepts appear on the graph of this polynomial function f(x)=x^4-5x^2

Step-by-step explanation:

How many x-intercepts?

Factoring this polynomial eases the job of counting the intercepts.

f(x)=x^4-5x^2 = x^2(x^2 - 5)

Setting x^2 = 0 leads to two x-intercepts:  (0, 0) and (0, 0) (a double root).

Setting x^2 - 5 = 0 yields the intercepts (-√5, 0) and (√5, 0).

Thus, there are, strictly speaking, FOUR x-intercepts.  Of these, three are immediately visible.