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Coolmath Algebra
Graphing Polynomials Lesson 6 - Multiplicities  (page 3 of 4)
---- This algebra lesson explains multiplicities and zeros.

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These powers are called multiplicities.

f ( x ) = ( x - 1 )^2 ( x + 4 )^3 ... ( x - 1 ) has a multiplicity of 2 and ( x + 4 ) has a multiplicity of 3

Let's do another one:

Find the real zeros of

f ( x ) = x^4 - 4x^2

then draw a rough sketch of the graph:

What's the basic shape?

f ( x ) = x^4 - 4x^2 ... basic 4th degree polynomial shape

What are the real zeros?

Solve    f ( x ) = 0

x^4 - 4x^2 = 0

We just need to do a little factoring...

x^2 ( x^2 - 4 ) = 0 gives x^2 ( x - 2 ) ( x + 2 ) = 0 which gives x^2 = 0 or x - 2 = 0 or x + 2 = 0 which gives x = 0 , x = 2 , and x = -2

real zeros: -2, 0 (kiss), 2
                multiplicity of 2

graph of f ( x ) = x^4 - 4x^2

Why don't you check this guy on the graphing calculator?

Enter it as  x^4-4x^2

(Your window may still be weird from the last guy we graphed...  hit the RESET button on the calculator to fix it.)

Continued on the next page

 The printing and distribution and/or downloading of these lessons is strictly prohibited.
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