The x-intercepts appear on this polynomial are 3 x intercepts.
Step-by-step explanation:
To find the x intercepts of the polynomial [tex]f(x)=x^{4} -5x^{2}[/tex] is by equating [tex]f(x)=0[/tex]
Thus, the equation becomes
[tex]\begin{array}{r}{x^{4}-5 x^{2}=0} \\{x^{2}\left(x^{2}-5\right)=0}\end{array}[/tex]
Equating, we get,
[tex]x^{2}=0,\left(x^{2}-5\right)=0[/tex]
[tex]x=0[/tex], [tex]\begin{aligned}x^{2}-5 &=0 \\x^{2} &=5 \\x &=\pm \sqrt{5}\end{aligned}[/tex]
Thus, the x-intercepts are [tex]x=0, x=\sqrt{5} , x=-\sqrt{5}[/tex]
Hence, the x-intercepts appear on this polynomial are 3 x intercepts.
