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Use the rational root theorem and synthetic devision. Given: f(x) = x^4 -10x^2 Given: f(x)=0 What are the roots to this polynomial? Write the polynomial in the factorized formula:

Respuesta :

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].

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