Factoring over the Complex Numbers, Answer 3

Exercise 3.

For which values of c does the polynomial

have two complex conjugate roots?

Answer.

The polynomial will have two complex conjugate roots if and only if its discriminant is negative. Since a=1 and b=4, the polynomial's discriminant is given by

The discriminant is negative, when c>4.

The polynomial will have two complex conjugate roots for c>4.

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Helmut Knaust
Tue Jun 24 09:48:17 MDT 1997