Descartes Rule of Sign

Example

x cubed has a positive sign, x squared negative, x negative, and 5 positive.

+ - - +

1 sign change from + to - and then another from - to +.

We have 2 sign changes.

Positive solutions are 2 or 0. You always have two choices from greater than or equal to 2.

(+) 2 or 0

Now make x negative.

- - + +

We have 1 sign change from - to +.

Therefore, (-) 1. We don't subtract 2 since, 1 or -1 solutions isn't possible. Only 1 is.

Since we had 2 or 0 positive, we must have 2 or 0 imaginary. This is because we know we have 1 negative and if there are 0 positive, we must have 2 imaginary.