Prove that if: x^n + a*x + b = 0, has a real solution, then it is unique.

Question

Let a and b be real numbers with a ≥ 0. Let also n be an odd integer with 0 ≤ n. Prove that if:

x^n + a*x + b = 0

has a real solution, then it is unique.

Answer 1

Here given that n is odd. We knw that odd degree polynomial has atleast one real root.

By discard sign rule

this equation has only one root(_ve)