MathDB
x^2 + 6x + 4a = 0 and x^2 + 2bx - 12 = 0 , have a common solution

Source: 1999 Estonia National Olympiad Final Round grade 9 p2

March 13, 2020
trinomialquadratic polynomialalgebra

Problem Statement

It is known that the quadratic equations x2+6x+4a=0x^2 + 6x + 4a = 0 and x2+2bx−12=0x^2 + 2bx - 12 = 0 have a common solution. Prove that then there is a common solution to the quadratic equations x2+9x+9a=0x^2 + 9x + 9a = 0 and x2+3bx−27=0x^2 + 3bx - 27 = 0.
Back to ProblemsView on AoPS