$6 x ^ { 4 } + 12 x ^ { 3 } + 6 x ^ { 2 } = 0$
A) -1,-1,0
B) 1,-1,0
C) 1,1,0
D) -1,1

Name: $6 x ^ { 4 } + 12 x ^ { 3 } + 6 x ^ { 2 } = 0$ A) -1,-1,0 B) 1,-1,0 C) 1,1,0 D) -1,1
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Question

$6 x ^ { 4 } + 12 x ^ { 3 } + 6 x ^ { 2 } = 0$
A) -1,-1,0 
B)  1,-1,0 
C)  1,1,0 
D)  -1,1

Quizplus · Accepted Answer

The equation can be factored as $6x^2(x^2 + 2x + 1) = 0$, simplifying to $6x^2(x + 1)^2 = 0$. The roots are $x = 0$ and $x = -1$ (with a multiplicity of 2 for -1), matching choice A.

6x4+12x3+6x2=06 x ^ { 4 } + 12 x ^ { 3 } + 6 x ^ { 2 } = 06x4+12x3+6x2=0

$6 x ^ { 4 } + 12 x ^ { 3 } + 6 x ^ { 2 } = 0$