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

`x=0`,
`x=√(5)` and
`x=-√(5)`.

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=(+-)√(5)`

Therefore, the roots are
`x=0`,
`x=√(5)` and
`x=-√(5)`.