Answer:
A) 2 + i
Step-by-step explanation:
F(x) = x^3 - 3x^2 + x + 5
0 = x^3 - 3x^2 + x + 5
0 = (x+1)(x^2 - 4x + 5)
Great, now we can separate these two parenthesis expressions because of the Zero Product Property. Start with the simple one:
0 = x + 1
x = -1
We have our first real root! But it doesn't look like that's one of the answer choices, so move on to the other expression:
0 = (x^2 - 4x +5)
This expression can't be factored, so we will use the quadratic formula (which is x = [tex]\frac{-b+-\sqrt{b^{2}-4ac } }{2a}[/tex]).
First solve for the positive part:
= (4 + sqrt(16-20)) / 2
= 4 + sqrt(-4) / 2
= 4 + 2i / 2
= 2 + i
Then for the negative part:
= (4 - sqrt(16-20)) / 2
= 4 - sqrt(-4) / 2
= 4 - 2i / 2
= 2 - i
2 + i is answer choice A! Our other roots, 2 - i and -1, aren't answer choices.
