# How do you use the rational root theorem to find the roots of #5x^4 + 9x^3 + 5x^2 + 2x + 4 = 0#?

##### 2 Answers

List the possible rational roots and then test them. None of them are roots.

#### Explanation:

For

The divisors of

The divisors of

So,the possible rational roots are:

Since all of the coefficients are positive, there can be no positive roots.

Testing by synthetic division we can find that

So we need to test

The equation has no rational roots.

Any rational roots must be

None of these are roots, so it has no rational roots.

#### Explanation:

Let

By the rational root theorem, the rational roots of

So the only possible rational roots are

None of these are roots, so there are no rational roots.

In fact

graph{5x^4+9x^3+5x^2+2x+4 [-11.99, 11.42, -1.56, 10.15]}