Using Intermediate Value Theorem and Rolle's Theorem, is there a way to show that x^4-4x+1 has exactly 2 real roots?
I have discovered that a root exists in the interval (0,1) and (1,2). So there must be at least two real roots to the equation. However, I am having difficulty continuing the proof to show that these are the only 2 real roots.
Any help would be appreciated.
Thanks in advance.