How do you find the zeros and multiplicity of $f (x) = {(x - 2)}^{4} (x - 3)$ $f(x)=(x-2)^4(x-3)$ ?

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How do you find the zeros and multiplicity of $f (x) = {(x - 2)}^{4} (x - 3)$ $f(x)=(x-2)^4(x-3)$ ?

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Answer 1 · 2017-05-25T13:38:38

$x = 2 multiplicity 4, x = 3 multiplicity 1$ $x=2" multiplicity 4", x=3" multiplicity 1"$

Explanation:

$zeros are the values of x that make f (x) = 0$ $"zeros are the values of x that make " f(x)=0$

$solve {(x - 2)}^{4} (x - 3) = 0$ $"solve " (x-2)^4(x-3)=0$

$equate each factor to zero$ $"equate each factor to zero"$

$(x - 2) = 0 \Rightarrow x = 2$ $(x-2)=0rArrx=2$

$\Rightarrow {(x - 2)}^{4} = 0 \Rightarrow x = 2 \leftarrow 4 times$ $rArr(x-2)^4=0rArrx=2larr" 4 times"$

$x - 3 = 0 \Rightarrow x = 3 \leftarrow 1 only$ $x-3=0rArrx=3larr" 1 only"$

$\Rightarrow x = 2 with multiplicity 4$ $rArrx=2" with multiplicity 4"$

$and x = 3 with multiplicity 1$ $"and " x=3" with multiplicity 1"$

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How do you find the zeros and multiplicity of $f (x) = {(x - 2)}^{4} (x - 3)$ $f(x)=(x-2)^4(x-3)$ ?

1 Answer

Explanation:

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How do you find the zeros and multiplicity of f(x)=(x-2)^4(x-3)f(x)=(x−2)4(x−3)f(x)=(x-2)^4(x-3)?

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Explanation:

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How do you find the zeros and multiplicity of $f (x) = {(x - 2)}^{4} (x - 3)$ $f(x)=(x-2)^4(x-3)$ ?