A partial solution set is given for the equation. $$x ^ { 4 } - 8 x ^ { 3 } + 13 x ^ { 2 } - 8 x + 12 = 0 ; \{ 6,2 \}$$
Find the complete solution set.
A) $6,2 , - i , i$
B) $6,2,0,0$
C) $6,6,6 , i$
D) $6,2 , - 2 i , 2 i$
E) none of these

Question

Quizplus · Accepted Answer

The given equation is a quartic equation. Since the partial solution set contains two real numbers, the other two solutions must be complex conjugates. Therefore, the complete solution set is $6,2 , - i , i$.

A Partial Solution Set Is Given for the Equation x4−8x3+13x2−8x+12=0;{6,2}x ^ { 4 } - 8 x ^ { 3 } + 13 x ^ { 2 } - 8 x + 12 = 0 ; \{ 6,2 \}x4−8x3+13x2−8x+12=0;{6,2}

A Partial Solution Set Is Given for the Equation $x ^ { 4 } - 8 x ^ { 3 } + 13 x ^ { 2 } - 8 x + 12 = 0 ; \{ 6,2 \}$