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Veseljchak [2.6K]
3 years ago
13

Which of the following is a root of the polynomial function below

Mathematics
1 answer:
VMariaS [17]3 years ago
8 0

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

<u>x = -1</u>

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

  <u>= 2 + i</u>

Then for the negative part:

= (4 - sqrt(16-20)) / 2

  = 4 - sqrt(-4) / 2

  = 4 - 2i / 2

  <u>= 2 - i</u>

<u></u>

<u>2 + i</u> is answer choice A! Our other roots, <u>2 - i</u> and <u>-1</u>, aren't answer choices.

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