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

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

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

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

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

Question

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

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

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

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

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

anonymous · Answer

one negative real root and two complex roots

anonymous · Answer

Descartes Rule of Signs
to find the max number of positive real zeros, just count the sign changes for f(x)
==> there are 2 sign variations (between the first and second terms the signs change; and between the second and third also).  The max of two can be less by a multiple of 2, names 2-2=0.

So the possible number of positive real zeros is 2 or 0.

anonymous · Answer

there is more to the theorem but there is only one answer with 2 or 0 for pos. (the third) so we are done.

anonymous · Answer

do you want me to continue? there's a bit more

anonymous · Answer

thanx champ, but if the answer is the 3rd i have so much work i dont want to drag it out anymore than i have to, you have been great i am sure i will be back, i HATE math, thank God for this site and for all you guyz i would just die if you all havent been helping me