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

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March 15, 2021
algebratrinomial

Problem Statement

Prove that if the numbers a,b,ca, b, c are the lengths of the sides of some nondegenerate triangle, then the equation b2x2+(b2+c2āˆ’a2)x+c2=0b^2x^2 + (b^2 + c^2 - a^2) x + c^2 = 0 has imaginary roots.
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