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Imaginary Numbers Homework -- Homework: Quadratic Equations and Complex Numbers

Module by: Kenny Felder

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

Note: Your browser may not currently support MathML. See our browser support page for additional details. You can always view the correct math in the PDF version.

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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