Polynomial has real roots – math.stackexchange.com

Polynomial has real roots – math.stackexchange.com

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I am trying to prove that the polynomial $f = X^3+pX+q \in \mathbb{R}[X]$ has three real roots iff $\Delta(f) = -(4p^3+27q^2) \geq 0$. I've figured out the left-to-right direction. Write $f = (X-\...

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