Question

f(x)=2x^4+5x^2-6x+9
Use Descartes' Rule of Signs to determine the possible numbers of positive and negative real zeros.

Answer 1

positive: two sign changes, max two real roots.
negative: zero sign changes, zero real roots

min number of non-real roots:
4-(2-0)=2

Answer 2

one flip in f(x) from 5 x^2 to - 6 x
second from -6 x to +9

no flips in f(-x) = 2x^4 + 5x^2 + 6x + 9

so two or zero positive real roots

check with
http://www.emathhelp.net/calculators/algebra-1/descartes-rule-of-signs-calculator/