MathDB

A student concentrates on solving quadratic equations in

\mathbb{R}

. He starts with a first quadratic equation

x^2 + ax + b = 0

where

a

and

b

are both different from 0. If this first equation has solutions

p

and

q

with

p \leq q

, he forms a second quadratic equation

x^2 + px + q = 0

. If this second equation has solutions, he forms a third quadratic equation in an identical way. He continues this process as long as possible. Prove that he will not obtain more than five equations.

Problem Statement