MathDB

Roots of two quadratic equations

Source: Germany 2021, Problem 1

June 16, 2021

quadraticsalgebraalgebra proposedquadratic equationroots

Problem Statement

Determine all real numbers

a,b,c

and

d

with the following property: The numbers

a

and

b

are distinct roots of

2x^2-3cx+8d

and the numbers

c

and

d

are distinct roots of

2x^2-3ax+8b