Sliding the Roots of Cubics

The roots of a cubic polynomial depend on the coefficients of the cubic in a complicated way. In this Demonstration, you move the roots in the complex plane by varying the coefficients of the cubic.

If the coefficients b, c, and d of a cubic (x^3)+b (x^2)+c x+d are real, the cubic will have either three real roots or one real root and a pair of roots that are complex conjugates of each other. For some combinations of coefficients, two roots will 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 conjugate roots.

THINGS TO TRY

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Contributed by: Robert Baillie

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