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

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) $x = 0 , \text { multiplicity } 1 ; x = 1 , \text { multiplicity } 1 ; x = - 1 , \text { multiplicity } 1 ; x = 6 \text {, multiplicity } 1$