1. The problem statement, all variables and given/known data Prove that the function 111x^111+11x^11+x+1 has exactly one real root. 3. The attempt at a solution Well, I know how to prove this. f is continuous because It's a polynomial. f(-1) equals -111-11-1+1 = -122 < 0 and f(0) equals 1. therefore, It satisfies all conditions of the intermediate value theorem and the theorem tells us that there must be a zero of f between -1 and 0. Now we can use Rolle's theorem to rule out any other possible real roots of the function. but the problem is the derivative of the function leads to an equation which can't be solved without a computer. so I can't show that the assumption that f has other real roots leads to a contradiction using Rolle's theorem. What can I do now?