R(x) = 2x^5 + 3x^3 + 2x^2 − 10

Question

List all possible rational zeros given by the Rational Zeros Theorem (but don't check to see which actually are zeros)

Answer 1

R(x) = 2x^5 + 3x^3 + 2x^2 − 10

Okay, there is the potential to have 5 zero roots because the equations are to the 5th level.

We have to look at the equation and see how often the sign changes.  there is only one.

R(x) = 2x^5 + 3x^3 + 2x^2 − 10

therefore there is only one positive root.

now multiply the equation by negative 1

R(x) = -2x^5 - 3x^3 - 2x^2 + 10

therefore there is only one negative root

So, there is one positive and one negative root, so far.

The value 0 may be a root or there may be 3 imaginery roots.