Question

Determine the possible number of negative zeros when f(x)=x^5 - 3x^3 + 2x^2 + 5x - 4

Answer 1

using Descartes' rule of signs

Count the number of sign changes in f(x)

+ \ - / + / + / -

There are 3 sign changes, hence a maximum of 3 possible positive roots

f( - x) = - $x^{5}$ + 3x³ + 2x² - 5x - 4

count the number of sign changes in f( - x)

- / + / + / - / -

There are 2 sign changes, hence a maximum of 2 possible negative roots