Problem #PRU-109041

Problems Methods Examples and counterexamples. Constructive proofs Pigeonhole principle Pigeonhole principle (other) Set theory and logic Theory of algotithms Theory of algorithms (other)
 13–16  4.0

Problem

x1 is the real root of the equation x2+ax+b=0, x2 is the real root of the equation x2−ax−b=0.

Prove that the equation x2+2ax+2b=0 has a real root, enclosed between x1 and x2. (a and b are real numbers).