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**wopashui** Show that if w is a root of the polynomial p(z), that is p(w)=0, where p(z) has real coefficients, then the conjugate of w is also a root of p(z).

I know that for polynomial of order 2, we can just use the quadratic formula, the two roots are conjugate of each other, but how do I prove it for general polynomial of order n?

the hint i was given is the conjugate of a is itself when a is real, and the conjugate of the product of 2 complex number is the product of each of the conjugate.