Question

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:

Answer 1

Answer:

$x=0$, $x=\sqrt{5}$ and $x=-\sqrt{5}$.

Step-by-step explanation:

The given polynomial is

$f(x)=x^{4}-10x^{2}$

Where $f(x)=0$

So, $x^{4}-10x^{2}=0$

First, we extract the greatest common factor

$x^{2} (x^{2} -10)=0$}

Then, we use the null property

$x^{2} =0 \implies x=0\\x^{2} -10=0 \implies x=(+-)\sqrt{5}$

Therefore, the roots are $x=0$, $x=\sqrt{5}$ and $x=-\sqrt{5}$.