Question

What are the possible number of positive, negative, and complex zeros of f(x) = -2x3 + 5x2 + 6x - 4 ?

Answer 1

it is a cube and since it has odd degree there must be at least one real zero

Answer 2

modified Descartes rule of signs
write down the signs for each term - + + -
check if it changes for f(x) when x >0; yes, no , yes possible 2 real positive
check if it changes for f(x) when x < 0: + + + - no no yes possible 1 real negative
highest power of function = 3 so 3 roots