Question

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

8, -14, and 3 + 9i

A. f(x) = x4 - 11x3 + 72x2 - 606x + 10,080

B. f(x) = x4 - 303x2 + 1212x - 10,080

C. f(x) = x4 - 11x3 - 72x2 + 606x - 10,080

D. f(x) = x4 - 58x2 + 1212x - 10,080

Answer 1

it wil have (x +14)(x - 8) as factors
there will be another zero 3 - 9i

Answer 2

divide these factors into the polynomial

Answer 3

im not actually sure how to do tht

Answer 4

right - i suspect its the last one D

you can use synthetic division also but i don't like that

(x +14)(x - 8) = x^2 + 6x - 112

x^2 -6x + 90
------------------
x^2+ 6x-112}x^4- 0x^3 - 58x^2 + 1212x - 10080
x^4 +6x^3 -112x^2
------------------
subtract -6x^3 + 54x^2 + 1212x
-6x^3 - 36x^2 + 672x
-------------------
subtract 90x^2 + 540x - 10080
90x^2 + 540x - 10080

Answer 5

ohh i see okay, th

Answer 6

thank you*

Answer 7

it was the correct one
so D = (x+14)(x-8)(x^2 -6x + 90)

the last part will have complex roots

x = 6 +/- sqrt(36 - 4*90) / 2

which will give you 3+ 9i and 3 + 9 i

Answer 8

i see, and totally get it now! thank you so much

Answer 9

yw