MathNet 2026 — Part 03 Question 183

Let $a, b, c$ be non-null real numbers and $a \neq b$. Prove that if equations $x^{2}+a x+b c=0$ and $x^{2}+b x+c a=0$ have a common root, then the remaining roots check the equation $x^{2}+c x+a b=0$.