Solving Cubic Equations and Inverses

A cubic equation is a polynomial equation of degree three, typically in the form of $$ax^3 + bx^2 + cx + d = 0$$ where a, b, c, and d are constants and a ≠ 0.

The general form of a cubic equation is $$ax^3 + bx^2 + cx + d = 0$$ .

The formula for the volume of a cylinder is $$V = \pi r^2 h$$ where r is the radius and h is the height.

The radius is half the length of the diameter. The diameter is the longest distance across the circle, passing through the center.

The volume of a sphere is given by the formula $$V = \frac{4}{3} \pi r^3$$ where r is the radius.

The inverse of a function reverses the input and output. If $$f(x) = y$$ , then the inverse function is denoted as $$f^{-1}(y) = x$$ .

To solve a cubic equation, you can use methods such as factoring, synthetic division, or applying the cubic formula.

Synthetic division is a simplified form of polynomial long division used to divide a polynomial by a linear factor.

The sum and product of the roots of a cubic equation can be related to its coefficients using Vieta's formulas.

For a cubic equation $$ax^3 + bx^2 + cx + d = 0$$ , if the roots are r1, r2, r3, then: r1 + r2 + r3 = -b/a, r1r2 + r2r3 + r3r1 = c/a, r1r2r3 = -d/a.