Question

What are the possible numbers of positive, negative, and complex zeros of f(x) = 2x3 – 3x2 + 4x + 5 ?
Answer

pos:3 or 1 neg:1 com:3 or 1

pos:1 or 0 neg:2 com:2 or 0

pos:2 or 0 neg:1 com:2 or 0

pos:3 or 0 neg:1 com:2 or 0

Answer 1

well lets see. i cant realy explain on how you can solve it but by looking at it i can tell i would most likely be pos:1 or0 Neg:2 com:2 or 0... does that help?

Answer 2

Use Descartes's rule of signs to solve the problem.

What you are looking for is for the number of times there is a change in sign between any two terms.

So in this equation you will see that there are two changes of sign, one between 2x^3 and 3x^2 and the other between3x^2 and 4x.

Two changes of sign gives you either two positive real zeros or an even number less than two positive real zeros. 2 positives or 2-2=0 positives

To find the negative real zeros, replace x with (-x) and count the number times the signs change between terms.

So you have the equation.

\[-2x ^{3}-3x ^{2}-4x+5\]

You will see that there is one change of sign between -4x and 5.

So you will have one real negative, since subtracting an even number would give you a negative number of zeros.

So your zeros will be either 2 positive real zeros and one negative real zero, or one negative real zero and 2 complex zeros.