What is the maximum number of x-intercepts that can be found on a graph with equation y = ax^5 + cx^2 + f, where a, c, and f are any real numbers?
A. 2
B. 3
C. 4
D. 5

I don't just want the answer, I want an explanation please so I could solve this on my own in the future

Question

What is the maximum number of x-intercepts that can be found on a graph with equation y = ax^5 + cx^2 + f, where a, c, and f are any real numbers?
 A. 2
 B. 3
 C. 4
 D. 5

I don't just want the answer, I want an explanation please so I could solve this on my own in the future

cwrw238 · Answer

since the degree of this equation is 5 there will be 5 zeroes of which some may not be real.
only real roots will be x-intercepts

cwrw238 · Answer

- but all may be real

anonymous · Answer

y'=Ax4+Bx=0
x=0 and alfa
so there are two extermum so the x-interaction maximum are three points.

anonymous · Answer

Thanks to you both, I think I got it!