Question

what are the possible numbers of positive, negative, and complex zeros of f(x)=-3x^4+5x^3-x^2+8x+4?
positive 2 or 0; negative 2 or 0; complex 4 or 2 or 0
Positive 1; negative 3 or 1; complex 2 or 0
Positive 3 or 1; negative 1; complex 2 or 0
positive 4 or 2 or 0; negative 2 or 0; complex 4 or 2 or 0

Answer 1

@ganeshie8 do you know how to do this?

Answer 2

@popcornfun

Answer 3

hint: use Descartes rule

Answer 4

@Majestic4321

Answer 5

You would count the number of sign changes when the expression is in descending order.
Each sign change represent 1 (possible) positive root.

Answer 6

Since complex roots come up in pairs (conjugates), 3 positive roots could mean 1 positive and two complex. We don't get to know using Descartes Rule of signs.
Other methods are necessary.