Find All Real Zeros of the Polynomial $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }$

question 57

Multiple Choice

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 8 x ^ { 3 } + 12 x ^ { 2 }$ and determine the mutiplicity of each.

• A) \(x = 0\), multiplicity \(2 ; x = - 2\), multiplicity \(1 ; x = - 6\), multiplicity 1
• B) \(x = 2\), multiplicity \(2 ; x = 6\), multiplicity 2
• C) \(x = 0\), multiplicity \(2 ; x = 2\), multiplicity \(1 ; x = 6\), multiplicity 1
• D) \(x = - 2\), multiplicity \(2 ; x = - 6\), multiplicity 2
• E) \(x = 0\), multiplicity \(1 ; x = 2\), multiplicity \(1 ; x = - 2\), multiplicity \(1 ; x = 6\), multiplicity 1

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