Sliding the Roots of Quadratics

The quadratic formula shows how the roots of a quadratic depend on the coefficients. In this Demonstration, you move the roots in the complex plane by varying the coefficients of the quadratic.

If the coefficients and of a quadratic are real (as they are in this Demonstration), the quadratic will have either two real roots or a pair of roots that are complex conjugates of each other. Watch the two roots slide along the real axis, then merge (forming a double root), then split and move off the real axis to become a pair of complex roots.