Problem proving x^4 + ax + b..... So I started working on some of these http://www.math.vt.edu/people/plinnell/Vtregional/exams.pdf problems for fun. The relevant problem is #7 from year 1983. The problem: If a and b are real, prove that x^4 +ax + b = 0 cannot have only real roots. I worked on it for a while, but was unable to prove this. Then I thought about the case when a=b=0. Certainly zero is a real number, and substituting zero in for a and b you get: x^4 = 0. Now the only solution to this is x = 0 (with multiplicity 4), which would mean that it only has real roots. I wanted to get other's opinions and since few of my friends like math I decided to come here and ask: Am I missing something or is the problem just wrong?