About Cubic Equation Formula
In mathematics, the cubic equation formula expresses the cubic equation. A cubic equation is a three-dimensional equation. All cubic equations' roots are either one real root and two imaginary roots or three real roots. Cubic polynomials are defined as polynomials with degree three.
What is Cubic Equation Formula?
The cubic equation formula is required to plot the curve of a cubic equation. The roots of a cubic equation can be found using this formula. There will be n number of roots if the polynomial's degree is n. The zeros in a cubic equation are also known as the roots.
The cubic equation formula is given by: ax3 + bx2 + cx + d = 0
Depressing the Cubic Equation
Substitute x = y - b/3a
in the above cubic equation, then we get, 
Simplifying further, we obtain the following depressed cubic equation – 
It must have the term in x3or it would not be cubic ( and so a≠0), but any or all of b, c and dcan be zero. For instance:
The examples of cubic equations are:
- x3 – 6x2 + 11x – 6 = 0
- 4x3 + 57 = 0
- x3 + 9x = 0
Solved examples of Cubic Equation Formula
Example:Solve x3– 6x2+ 11x – 6 = 0
Sol:This equation can be factorized to give
(x-1)(x-2)(x-3)=0
This equation has three real roots, all different – the solutions are x = 1, x = 2 and x = 3.
Example:Solve the cubic equation x3– 23x2+ 142x – 120.
Sol: First factorize the polynomial to get;
x3– 23x2+ 142x – 120 = (x – 1) (x2– 22x + 120)
But x2– 22x + 120 = x2– 12x – 10x + 120
= x (x – 12) – 10(x – 12)
= (x – 12) (x – 10)
Therefore, x3 – 23x2 + 142x – 120 = (x – 1) (x – 10) (x – 12)
Equate each factor to zero to get;
x = 1
x = 10
x = 12
The roots of the equation are x = 1, 10 and 12.
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