# How do you use the Rational Zeros theorem to make a list of all possible rational zeros, and use the Descarte's rule of signs to list the possible positive/negative zeros of #f(x)=-17x^3+5x^2+34x-10#?

##### 1 Answer

#### Explanation:

The pattern of signs of

The sign pattern of

The rational roots theorem says that we can find all the rational roots of a polynomial by taking

I will begin by looking at the negative values, since I know the polynomial has a negative root. Unfortunately none of the negative values are roots, so the negative root must be irrational.

Now we'll have to hope that there are two positive roots, and that at least one of them is rational. If we try all the positives, we find that

Now we set the other factor equal to zero to find its roots:

This matches up with our conclusions using Descartes' rule, since we ended up with