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A very general method for any polinomial is the rational root test: Any rational zero of $a x^2 + b x + c$ must be of the form $p / q$, where $p$ is a factor of $c$ and $q$ a factor of $a$ (don't forget signs!). This affords a factor $q x - p$, for a quadratic the other must be $(a / q) x - (c / p)$. As a bonus point, the (simple) proof of the test and the ...

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