Question

Write a polynomial function of minimum degree with real coefficients whose zeros include those listed. Write the polynomial in standard form.


7, -11, and 2 + 8i

Answer 1

Hint: Multiply f(x) = (x - 7)(x + 11)(x - (2 + 8i))

Answer 2

Um I am a bit unsure, I mulitpled the first part and got (x^2+4x-77) but how do I multiply w (x - (2 + 8i)?

Answer 3

(x - (2 + 8i)) = (x - 2 - 8i)

Answer 4

(154+616 i)-(85+32 i) x-79 x^2+x^3 ?

Answer 5

@Hero

Answer 6

Wolfram alpha's version:

http://www.wolframalpha.com/input/?i=expand+%28x+-+7%29%28x+%2B+11%29%28x+-+%282+%2B+8i%29%29

Answer 7

but these are my choices:

f(x) = x4 - 9x3 - 56x2 + 290x - 5236

f(x) = x4 - 9x3 + 56x2 - 290x + 5236

f(x) = x4 - 145x2 + 580x - 5236

f(x) = x4 - 25x2 + 580x - 5236

Answer 8

Try this:
f(x) = (x - 7)(x + 11)(x - (2 + 8i))(x + (2 + 8i))

Answer 9

yeah because on wolfram, what you are giving me has the same zeros as my problem...so
idk..

Answer 10

Well, that's the clue then

Answer 11

Use wolfram alpha to figure out which one of your answer choices also has the same zeroes.

Answer 12

Wolframalpha calculated the zeroes of the polynomial we came up with:
http://www.wolframalpha.com/input/?i=solve+%28x+-+7%29%28x+%2B+11%29%28x+-+%282+%2B+8i%29%29%28x+%2B+%282+%2B+8i%29%29+%3D+0

Answer 13

If you use wolframalpha in the same manner for the other possible answer choices, you should be able to find the polynomial that has the same zeroes. Once you find it, that will be the correct choice.

Answer 14

ended up f(x) = x4 - 25x2 + 580x - 5236

thanks for your help :) finished my work lol

Answer 15

I just realized that I wrote the original one down wrong. It should have been:

f(x) = (x - 7)(x + 11)(x - 2 + 8i)(x - 2 - 8i) = 0

Answer 16

^If you multiply that out, you get x^4 - 25x^2 + 580x - 5236

Answer 17

oh lol. well you were better than me anyway :p