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
I really don't know how toowrk it out on paper, I'm afraid. I just looked at it, and somehow knew that the answers are 7 and 9.
You can use Soh Cah Toa to get your answer, in other words, sin cos tan. If you already have x, that means you probably used tan, which is adjacent and opposite. Now for y, you are trying to find the hypotenuse so you could use, sin or cos, for sin you would use the adjacent (x) and the hypotenuse (y) and for cos, you would use opposite (4) and the hypotenuse (y). This is all based on the angle 45.
Variables represent unknowns. They are often letters (like x) but can also be other symbols like Greek numerics.
Hope this helps!!
