# How do you find the rational roots of #x^4+5x^3+7x^2-3x-10=0#?

##### 1 Answer

Use the rational roots theorem to find rational roots

#### Explanation:

Let

The rational roots theorem tells us that all rational roots of

So the possible rational roots are:

Note that the sum of the coefficients of

So

That is

We also find

So

We can long divide

A quick check of the discriminant of this quotient polynomial finds:

So there are no more real roots and no more linear factors with real coefficients.