![]() ![]() Should the polynomial have a rational root, this method will find it. If your polynomial has rational coefficients, try performing the rational root test (or use the rational zeros calculator to do it for you). To perform the division, you may want to use the method described in the synthetic division calculator.īut how to find the initial root? Well, there are no easy and 100% successful recipes. Then you need to divide your cubic polynomial by x − q x - q x − q to arrive at a quadratic polynomial. If you are somehow able to determine one root, then finding the other two poses no problem since your task reduces to solving a quadratic equation, which you can do either by factoring (as in the factoring trinomials calculator) or by using the quadratic formula. Fortunately, there's Omni's cubic equation calculator, which can find the roots of any cubic equation in no time! It's definitely more complicated than in the case of quadratic trinomials, where we have the well-known quadratic formula. In general, finding the roots of cubic equations may be challenging. In the latter case, they are a pair of conjugate numbers, i.e., their real parts are equal, and their imaginary parts have opposite signs. The other two roots might be real or complex. Has a root 0 0 0 with multiplicity three.Ī cubic equation always has at least one real root. Some of these roots, however, may be equal. It follows from the fundamental theorem of algebra that every cubic equation has exactly three complex roots. A root of a cubic equation is every argument x x x that satisfies this cubic equation.Ģ 3 − 8 = 8 − 8 = 0 2^3 - 8 = 8 - 8 = 0 2 3 − 8 = 8 − 8 = 0. ![]()
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