MathDB
P(x) = ax^4 - 8ax^3 + bx^2 - 32cx + 16c has 4 positive real roots

Source: 2023 NZMO - New Zealand Maths Olympiad Round 1 p8

September 2, 2023
polynomialalgebra

Problem Statement

Find all non-zero real numbers a,b,ca, b, c such that the following polynomial has four (not necessarily distinct) positive real roots. P(x)=ax4−8ax3+bx2−32cx+16cP(x) = ax^4 - 8ax^3 + bx^2 - 32cx + 16c
Back to ProblemsView on AoPS