# Algorithm to determine if a polynomial has any complex roots

Is there a simple algorithm to determine if a given polynomial (with all real coefficients) has all real roots? I do not need to know what the roots are; I just what to know if a given polynomial has any complex roots.

Background: I am aware that there are algorithms (for example see here) to compute all of the real roots of an arbitrary degree polynomial $$$$\label{polynomial} a_0 + a_1x + a_2x^2 + \cdots + a_n x^n ,$$$$ where $$a_0,...,a_n$$ are all real constants.