MathDB

Quadratic equations

Source: Czech and Slovak Olympiad 1963, National Round, Problem 4

June 17, 2024

quadratic polynomialReal Rootsrootsquadraticsalgebra

Problem Statement

Consider two quadratic equations \begin{align*}x^2+ax+b&=0, \\ x^2+cx+d&=0,\end{align*} with real coefficients. Find necessary and sufficient conditions such that the first equation has (real) roots

x,x_1,

the second

x,x_2

and

x>0,x_1>x_2

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