Question

Using Descartes’ rule of signs, which statement about this function is true?
f(x)= x^4 – 2x^3 + 4x^2 – 2

Answer 1

There are 3 possible real positive roots.

Answer 2

Actually there are either 3 possible real positive roots or 1 real positive root; there is only one possible negative root.

Answer 3

Your possibilities are as follows:

Answer 4

Your total possibilities have to add up to 4 cuz you have a 4th degree polynomial. For the positive roots you have a possibility of 3 or 3-2=1. You always subtract 2 to get the other option for the roots. For the negative roots, you only have a possibility of 1 because 1-2=-1 and you can't have a negative number of negative roots.