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

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):. a = b = c = . 10. Example: Solve 0 = 2 x 2 – 2 x + 10. 1. -2.

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

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

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

  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 Complex Roots because it has no x-intercepts 2 Real Roots because it has two x-intercepts A 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. Complex Conjugates 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 – 3iand 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 + 10 and Complex Conjugates!

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