## which of the following is a root of the polynomial function below F(x)= x^3 – 3x^2 + x + 5 A) 2+I B) 1 C) 2 D

Question

which of the following is a root of the polynomial function below
F(x)= x^3 – 3x^2 + x + 5
A) 2+I
B) 1
C) 2
D)-2+i

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5 months 2021-12-30T21:42:46+00:00 1 Answer 0 views 0

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 = $$\frac{-b+-\sqrt{b^{2}-4ac } }{2a}$$).

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.