Answer:
[tex]x=0[/tex], [tex]x=\sqrt{5}[/tex] and [tex]x=-\sqrt{5}[/tex].
Step-by-step explanation:
The given polynomial is
[tex]f(x)=x^{4}-10x^{2}[/tex]
Where [tex]f(x)=0[/tex]
So, [tex]x^{4}-10x^{2}=0[/tex]
First, we extract the greatest common factor
[tex]x^{2} (x^{2} -10)=0[/tex]}
Then, we use the null property
[tex]x^{2} =0 \implies x=0\\x^{2} -10=0 \implies x=(+-)\sqrt{5}[/tex]
Therefore, the roots are [tex]x=0[/tex], [tex]x=\sqrt{5}[/tex] and [tex]x=-\sqrt{5}[/tex].
