Question

Find all real zeros (if any) and state the multiplicity of each.
f(x)=x5(x−3)2(x+8)

Answer 1

• x = 0 multiplicity of 5

• x = 3 multiplicity of 2

• x = -8 multiplicity of 1

Explanation:

We are given an equation:

• 
  `f(x)=x^5(x-3)^2(x+8)`

And we are asked to find all real zeros and state the multiplicity of each.

• When f(x) = 0, the values of x are the zeros of a function.

To find the real zeros, you need set each variable equal to zero, the solve for the variable x.

The exponents value is the multiplicity of the zeros.

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`x^(5) =0`

`\sqrt[5]{x^5} =\sqrt[5]{0} \\`

x = 0 multiplicity of 5

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`(x-3)^2=0`

`\sqrt[2]{(x-3)^2} =\sqrt[2]{0} \\x-3 = 0\\`

x = 3 multiplicity of 2

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`(x+8)=0`

x = -8 multiplicity of 1

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