10.3 - Polynomial equations

Before reading this section you may want to review the following topics: To solve a polynomial equation, follow these steps:


Example: Solve the polynomial equation 16 x 3 − 13 x = 3.

Solution: First put the polynomial equation into standard form:
16 x 3 − 13 x − 3 = 0.
Factor the left-hand-side using the deflation method:
(x − 1) (4x + 1) (4 x + 3) = 0.
Set each factor equal to zero. This gives a set of equations:
x − 1 = 0
4x + 1 = 0
x + 3 = 0
Solve them. This gives a set of solutions:
x = 1
x = −¼
x = −¾
The solution set is x = {1,   −¼,   −¾}.



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