Question

What does​ Descartes' rule of signs tell you about the possible number of positive real zeros and the possible number of negative real zeros of the​ function?
f(x)=3x^5-3x^2+x-4

The possible number of positive real zeros is
what?​ the possible number of negative real zeros is
what?

Answer 1

Answer:

• 3 or 1 positive real zeros
• 0 negative real zeros

Step-by-step explanation:

The signs of the coefficients of the given terms are ...

  +  -  +  -

There are three sign changes, so the number of positive real zeros is 3 or 1.

When odd-degree terms have their signs changed, the signs become ...

  -  -  -  -

There are no sign changes, hence no negative real zeros.

_____

A graph confirms this evaluation.