Copy of Imaginary Roots
- Author:
- Emily Gorman, Scott Farrar
Drag the parabola to observe the real and imaginary parts to the roots.
www.scottfarrar.com | @farrarscott
Because this parabola opens upward, where does the vertex have to be for there to be two real roots?
If the parabola opened downward, where would the vertex have to be for the parabola to have two real roots?
Whether or not a parabola opens upward or downward, when will it have only one real root? (A double root.)
Describe what conditions would prevent a parabola from having any real roots. Discuss its position on the coordinate plane and the discriminant.
Describe the relative positions of the two complex roots on the complex plane.
Consider the quadratic formula. Why does it make sense that the complex roots of a quadratic equation would have identical real components and opposite imaginary components?