Solves cubic equations of the form ax³ + bx² + cx + d = 0
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A cubic equation is a polynomial equation of degree 3, having the general form:
Where a, b, c, and d are constants, and a ≠ 0.
A cubic equation can have:
This is an algebraic method for solving cubic equations developed by Gerolamo Cardano in the 16th century.
If one root is known, synthetic division can be used to reduce the cubic to a quadratic equation.
For complicated equations, numerical methods like Newton-Raphson can be used to approximate the roots.
The discriminant of a cubic equation can help determine the nature of its roots:
Coefficients: a=1, b=-6, c=11, d=-6
This equation can be factored as: (x-1)(x-2)(x-3) = 0
The roots are: x = 1, x = 2, and x = 3
Coefficients: a=1, b=0, c=-3, d=2
This equation has one real root (x = -1) and two complex roots