The Cubic and Quartic Formulas
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Formulas to Fear
In Algebra, we are taught the Quadratic Formula as a failsafe way to solve any quadratic equation. All we had to do was rearrange the quadratic equation so that all the terms were on one side, which made the equation look like$$ax^2 +bx +c = 0$$An equation of this form had potentially two solution:$$x = \frac{-b + \sqrt{b^2-4ac}}{2a}$$and$$x = \frac{-b - \sqrt{b^2-4ac}}{2a}$$Similarly, any third degree (cubic) equation, once arranged to be equal to zero, has three definitive formulaic solutions.A cubic equation arranged to be equal to zero can be expressed as$$ax^3 + bx^2 + cx + d = 0$$The three solutions to this equation are given by the Cubic Formula. The first solution is the one that is certain to be real (all odd degree polynomials have at least one real root) and the other two may or may not be real.- Popular Content Misfit Math »