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It depends on the domain. In the complex domain, a polynomial of order n must have n solutions, although some of these may be multiple solutions.

In the real domain, a polynomial of odd order must have at least one real solution, while a polynomial of even order may have no real solutions.

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Q: Can a polynomial equation have no answer?
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Related questions

Who discovered polynomial?

In the 1880s, Poincaré created functions which give the solution to the order polynomial equation to the order of the polynomial equation


What is the difference between a polynomial and a quadratic equation?

A quadratic equation is of degree 2, that is, the highest power is 2. A polynomial is not an equation, however, you can convert it into an equation by setting the polynomial equal to zero for example. A polynomial EQUATION can be of any degree: 1, 2, 3, 4, etc.


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Is an algebraic equation the same as a polynomial equation?

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No. A polynomial can have as many degrees as you like.


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