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Homework: Quadratic Equations and Complex Numbers

Module by: Kenny M. Felder. E-mail the author

Summary: This module provides practice problems related to solving quadratics containing imaginary numbers.

I’m sure you remember the quadratic formula: x = −b±b2−4ac2ax=−b±b2−4ac2a size 12{ { { - b +- sqrt {b rSup { size 8{2} } - 4 ital "ac"} } over {2a} } } {}. Back when we were doing quadratic equations, if we wound up with a negative number under that square root, we just gave up. But now we can solve these equations!

Exercise 1

Use the quadratic formula to solve: 2 x 2 + 6 x + 5 = 0 2 x 2 +6x+5=0.

Exercise 2

Use the quadratic formula to solve: x 2 - 2 x + 5 = 0 x 2 -2x+5=0.

Exercise 3

Check one of your answers to #2.

Exercise 4

Solve by completing the square: 2 x 2 + 10 x + 17 = 0 2 x 2 +10x+17=0.

Exercise 5

  • a. In general, what has to be true for a quadratic equation to have two non-real roots?
  • b. What is the relationship between the two non-real roots?
  • c. Is it possible to have a quadratic equation with one non-real root?

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