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### Why do cubic equations always have at least one real root, and why was it needed to introduce complex numbers?

You ask in a comment I am not sure, because if it was a real root, then I don't understand why this is used as an argument for introducing complex numbers? Having a real root feels unrelated to ...
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### Why do cubic equations always have at least one real root, and why was it needed to introduce complex numbers?

I don't understand why a cubic always has at least one real root. I don't see why the reason is "since $y^3 − py − q$ is positive for sufficiently large positive $y$ and negative for ...
• 9,418

### Why do cubic equations always have at least one real root, and why was it needed to introduce complex numbers?

(this is just a simple historical explanation, without delving in the theory of cubic equations) The trouble with the solution of the cubic equation is that when the equation has three real solutions ...
• 9,944
First you were asking about: I don't see why the reason is "since $y^3 − py − q$ is positive for sufficiently large positive $y$ and negative for sufficiently large negative $y$)." Answer ...