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Polynomial Equations and Functions:
A polynomial equation or function with degree n has n number
of solutions; for example, a polynomial with a degree of three
has three solutions.
ex.
(x - 4)3(x + 7)2(x + 2) = 0
This equation has a degree of six
This can also be written as:
(x - 4)(x - 4)(x - 4)(x + 7)(x + 7)(x + 2) = 0
which implies that there are six solutions to the equation:
| x-4 = 0 |
or |
x-4 = 0 |
or |
x-4 = 0 |
| x = 4 |
or |
x = 4 |
or |
x = 4 or |
| x+7 = 0 |
or |
x+7 = 0 |
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| x = -7 |
or |
x = -7 |
or |
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| x+2 = 0 |
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| x = -2 |
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The general solution for the equation is{4,-7,-2}, but it is
also said that the equation has a solution 4 with multiplicity of
three, a solution -7 with multiplicity of two.
Multiplicity is a repetitive solution to an equation, from the
above example, the solution 4 has a multiplicity of three,
meaning that the solution 4 is repeated three times.
Any solution of multiplicity p is counted p
times.
Solving Polynomial Equations( with degree 3 or greater):
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