P(x) = 9x^3 − 7x^2 + 8x − 8

Question

Use Descartes' Rule of Signs to determine how many positive and how many negative real zeros the polynomial can have. Then determine the possible total number of real zeros. (Enter your answers as comma-separated lists.)

P(x) = 9x^3 − 7x^2 + 8x − 8

number of positive zeros
number of negative zeros
number of real zeros

Answer 1

3 sign changes for positive values 3 sign changes; for negative values, none.

In fact there is a single positive real root.

Please note , for this kind of a question, graphing is always helpful.