x-intercepts are the points where the graph crosses the x-axis. Along the x-axis value of y-coordinate is zero. So if we equate the given equation to 0, we can find the points where y-coordinate is zero and thus we can find the x-intercepts of F(x).
[tex]0= x^{4}- 5^{2} \\ \\
25= x^{4} \\ \\
[/tex]
Taking square root of both sides we get:
[tex](5) = x^{2} , \\ -5= x^{2} [/tex]
The square root of -5 will result in a complex number. So we reject this value and only consider [tex]5= x^{2} [/tex]
Taking the square root again, we get:
[tex]+- \sqrt{5}=x [/tex]
Thus the F(x) has two x-intercepts at [tex]x= \sqrt{5} [/tex] and [tex]x= -\sqrt{5} [/tex]
