Thread: inequalities II

Prove that if real numbers a, b and c satisfy

a + b + c > 0,

ab + ac + bc > 0

and

abc > 0,

then each of a, b and c is positive.

I'll give you a tip: a b c are the roots of the 3rd degree polynomial a X^3 + b X^2 + c X + d

S1 = a + b + c = -b/a > 0
S2 = ab + ac + bc = c/a > 0
S3 = abc = -d/a > 0

i'll to think a bit for the rest of the problem