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x^3 + ax^2 + bx + c = 0 has real roots

Source: Polish MO Finals 1964 p4

August 30, 2024
algebrapolynomial

Problem Statement

Prove that if the roots of the equation x3+ax2+bx+c=0 x^3 + ax^2 + bx + c = 0 , with real coefficients, are real, then the roots of the equation 3x2+2ax+b=0 3x^2 + 2ax + b = 0 are also real.
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