Using the Quadratic Formula to Find Complex Roots (Including Complex Conjugates)

Complex Number A number consisting of a real and imaginary part. Usually written in the following form (where a and b are real numbers): Example: Solve 0 = 2x2 – 2x + 10 a = b = c = 1 -2 10

Classifying the Roots of a Quadratic Describe the amount of roots and what number set they belong to for each graph: 1 Repeated Real Root because it has one x-intercept (bounces off) 2 Real Roots because it has two x-intercepts 2 Complex Roots because it has no x-intercepts A Quadratic ALWAYS has two roots

Determining whether the Roots are Real or Complex What part of the Quadratic Formula determines whether there will be real or complex solutions? Discriminant < 0

The sum and product of complex conjugates are always real numbers For any complex number: The Complex Conjugate is: The sum and product of complex conjugates are always real numbers Example: Find the sum and product of 2 – 3i and its complex conjugate.

Complex Roots Are Complex Conjugates A quadratic equation y = ax2 + bx + c in which b2 – 4ac < 0 has two roots that are complex conjugates. Example: Find the zeros of y = 2x2 + 6x + 10 and Complex Conjugates!