4

Part of 1963 Czech and Slovak Olympiad III A

Problems(1)

Quadratic equations

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

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,

x,x_2

x>0,x_1>x_2

quadratic polynomialReal Rootsrootsquadraticsalgebra