Solve Third Degree Polynomial Equation

Introduction:

Polynomial expression is constructed from variables and constants and it has finite length. Variables are also known as indeterminants. Polynomial expressions consists only the operations of addition, subtraction, multiplication and non-negative, whole number exponents. (source: Wikipedia)

Polynomial Function of the Third Degree:

A third degree polynomial function is in the format of :

f(x) = ax³ + bx² + cx + d

Steps for help solving third degree polynomial equation:

The easiest methos to solving a polynomial equation is,

• Find the rational root
• Use synthetic division

Example 1:

Solving the third degree polynomial equation 4 x ³ − 3x ² − 25x − 6.

Solution:

This polynomial can be factored and written as,

4x³ − 3x² − 25x − 6 = (x − 3) (4x + 1) (x + 2)

So we can see that a 3rd degree polynomial has 3 roots.

The associated polynomial equation is obtained by setting the polynomial equal to zero:

f(x) = 4x³ − 3x² − 25x − 6 = 0

In factored form, this is:

(x − 3) (4x + 1) (x + 2) = 0

Separate the above factors and equate to zero, we get

x - 3 = 0

x = 3

4x + 1 = 0

x = - 1 / 4

x + 2 = 0

x = - 2

Hence the roots are x = 3, (- 1 / 4) , − 2.