Question

Which answer best describes the complex zeros of the polynomial function?

f(x)=x3+x2−8x−8

A. The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly one location.

B. The function has one real zero and two nonreal zeros. The graph of the function intersects the x-axis at exactly two locations.

C. The function has three real zeros. The graph of the function intersects the x-axis at exactly three locations.

D. The function has two real zeros and one nonreal zero. The graph of the function intersects the x-axis at exactly one location.

Answer 1

@silvernight269 @563blackghost

Answer 2

@Shadow

Answer 3

\[f(x)=x^3+x^2−8x−8\]
\[f(x) = x^2 (x + 1) -8(x +1)\]
\[f(x) = (x^2 - 8)(x+1)\]
\[0 = (x^2 - 8)(x+1)\]
\[x^2 - 8 = 0\]
\[x^2 = 8\]
\[x = \pm \sqrt 8 = \pm 2 \sqrt 2\]
\[x + 1 = 0\]
\[x = -1\]

Answer 4

Does that work look familiar to what you have done in lessons?

Answer 5

yes

Answer 6

Okay so then based on that, what do you think the answer is?

Answer 7

the answer is A

Answer 8

The answer would be A if it were x^2 + 8, because that would make for:

\[\pm 2i \sqrt 2\]
Two imaginary numbers. But that is not the case.

Answer 9

CORRECT

Answer 10

So if all the numbers are real, what would the answer be.

Answer 11

With:
\[x = -1, 2 \sqrt 2, -2\sqrt 2\]

Answer 12

A

Answer 13

The answer would be A if it were:
\[x = -1, 2i \sqrt 2, -2i \sqrt 2\]

Answer 14

oh D

Answer 15

"The function has two real zeros and one nonreal zero."

But I said all the numbers are real. Lol stop guessing.

Answer 16

no i was between both A or D because i knew B and C were out of the questions so it had to have been either A or D i thought it was D at first then thought A i should've followed my first mind

Answer 17

It's C cause all the zeroes are real...

Answer 18

ok thank you on this shadow

Answer 19

shadow could you help me on my new question please