# How do you use the rational root theorem to find the roots of #3x^4 + 5x^3 + 3x^2 - 7x + 9 = 0#?

##### 2 Answers

There are no rational roots.

#### Explanation:

Rational roots would be the factors of

From the rational root theorem we find that the only possible rational roots are

None of these is a root, so the equation has no rational roots.

#### Explanation:

By the rational root theorem, any rational root of

That means that the only possible rational roots are:

Let

Then:

So none of the possible rational roots is a root of

So

In fact it has no real roots at all:

graph{3x^4+5x^3+3x^2-7x+9 [-20, 20, -4, 16]}