query: Show that any complex roots must occur in conjugate pairs.
positive_passages.docid: 154393
positive_passages.text: Roots of polynomial with real coefficients appear in conjugate pairs.
negative_passages.docid: 36937
negative_passages.text: How to find a starting point for root finding in complex plane?
negative_passages.docid: 118085
negative_passages.text: complex polynomial satisfying inequality
negative_passages.docid: 69067
negative_passages.text: Principal $n$th root of a complex number
negative_passages.docid: 6484
negative_passages.text: Polynomials in one variable with infinitely many roots.
negative_passages.docid: 103662
negative_passages.text: How to prove that $B^\vee$ is a base for coroots?
negative_passages.docid: 131881
negative_passages.text: Show that the roots of P' lie in the same half plane as the roots of P
negative_passages.docid: 141677
negative_passages.text: Definition of complex conjugate in complex vector space
negative_passages.docid: 92609
negative_passages.text: How to Mathematically Prove the Bilinear Pairing Properties
negative_passages.docid: 24912
negative_passages.text: Show that if $fd'=f'd $ and the pairs $f, d $ and $f',d' $ are coprime, then $f=f' $ and $d=d' $.
negative_passages.docid: 86882
negative_passages.text: Proving Gauss' polynomial theorem (Rational Root Test)
negative_passages.docid: 140009
negative_passages.text: Show complex solutions exist
negative_passages.docid: 46493
negative_passages.text: Equation with conjugate (complex numbers)
negative_passages.docid: 13981
negative_passages.text: Proof that every polynomial of odd degree has one real root
negative_passages.docid: 139979
negative_passages.text: Proof there is a rational between any two reals
negative_passages.docid: 2408
negative_passages.text: Show that a polynomial has at least one positive solution/root.
negative_passages.docid: 6582
negative_passages.text: Prove the existence of the square root of $2$.