Presentation on theme: "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."— Presentation transcript:
1 Using the Quadratic Formula to Find Complex Roots (Including Complex Conjugates)
2 Complex NumberA 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 + 10a = b = c =1-210
3 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-intercepts2 Complex Roots because it has no x-interceptsA Quadratic ALWAYS has two roots
4 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
5 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 numbersExample: Find the sum and product of 2 – 3i and its complex conjugate.
6 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 + 10andComplex Conjugates!