1

Part of 1953 Polish MO Finals

Problems(1)

1/(x - a) +1/(x - b)+ 1/(x - c)= 0

Source: Polish MO Finals 1953 p1

Test whether equation

\frac{1}{x - a} + \frac{1}{x - b} + \frac{1}{x - c} = 0,

a

b

c

denote the given real numbers, has real roots.

algebrapolynomial