Find All Real Zeros of the Polynomial $f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 27 x ^ { 2 }$

question 122

Multiple Choice

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 12 x ^ { 3 } + 27 x ^ { 2 }$ and determine the multiplicity of each.

• A) \(x = 0 \text {, multiplicity } 1 ; x = 9 , \text { multiplicity } 1 ; x = - 9 , \text { multiplicity } 1 ; x = 3 \text {, multiplicity } 1\)
• B) \(x = 0 \text {, multiplicity } 2 ; x = 9 \text {, multiplicity } 1 ; x = 3 \text {, multiplicity } 1\)
• C) \(x = 0 \text {, multiplicity } 2 ; x = - 9 \text {, multiplicity } 1 ; x = - 3 \text {, multiplicity } 1\)
• D) \(x = 9 , \text { multiplicity } 2 ; x = 3 , \text { multiplicity } 2\)
• E) \(x = 0 \text {, multiplicity } 1 ; x = 9 , \text { multiplicity } 1 ; x = - 9 , \text { multiplicity } 1 ; x = 3 \text {, multiplicity } 1\).

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