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

Answer 1

use descartes sign rule
for f(x) there are 2 sign changes, so possible 2 positive real roots or 0 positive real roots (in which case you have 2 complex roots).
for f(-x) = -2x^3 -3x^2 -4x + 5 has 1 sign change, so it has exactly 1 negative real root. (must be real since complex roots come in pairs)

Answer 2

Kewl thx :)

Answer 3

wheres my medal?

Answer 4

lol hahaha