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Part of 1949-56 Chisinau City MO

Problems(1)

Chisinau MO p18 1949-56 VIII-IX b^2x^2+(b^2+c^2-a^2)x+c^2 = 0 imaginary roots

Source:

Prove that if the numbers

a, b, c

are the lengths of the sides of some nondegenerate triangle, then the equation

b^2x^2 + (b^2 + c^2 - a^2) x + c^2 = 0

has imaginary roots.

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