Answer:
Option B
Step-by-step explanation:
Complex roots occur as conjugate pairs so the third root is -3 - i ( note that the sign changes from + to -).
So in factor form we have:-
(x - 2)(x - (-3 + i))(x - (-3 - i)) = 0 Let's expand the last 2 factors first:-
(x - (-3 + i))(x - (-3 - i))
= (x + 3 - i)(x + 3 + i)
= x^2 + 3x +ix + 3x + 9 + 3i - ix - 3i - i^2
= x^2 + 6x + 9 - (-1)
= x^2 + 6x + 10
Now multiplying by (x - 2):-
(x - 2)(x^2 + 6x + 10) = 0
x^3 + 6x^2 + 10x - 2x^2 - 12x - 20 = 0
x^3 + 4x^2 - 2x - 20 = 0 (answer)
Option B
