Find All Real Zeros of the Polynomial $f ( x ) = x ^ { 4 } + 7 x ^ { 3 } + 6 x ^ { 2 }$

question 315

Multiple Choice

Find all real zeros of the polynomial $f ( x ) = x ^ { 4 } + 7 x ^ { 3 } + 6 x ^ { 2 }$ and determine the multiplicity of each.

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

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