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

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

anonymous · Answer

these are the choices
 f(x) = x4 - 11x3 + 72x2 - 606x + 10,080

 f(x) = x4 - 303x2 + 1212x - 10,080

 f(x) = x4 - 11x3 - 72x2 + 606x - 10,080

 f(x) = x4 - 58x2 + 1212x - 10,080

amistre64 · Answer

subtract x from each root, and multiply the whole mess together.

since they are suggesting a 4th degree poly, you might want to include the conjugate of that complex number

amistre64 · Answer

8-x, -14-x, and 3 + 9i-x

(8-x)(-14-x)(3+9i-x)  produces a x^3 function that has complex issues ...

if we include the conjugate we obtain:

(8-x)(-14-x)(3+9i-x)(3-9i-x)  which gets us to one of the options

anonymous · Answer

I got the first portion which is x^2+6x-112, but i can't seem to get the portion pertaining to 3+9i-x

amistre64 · Answer

this makes the drudgery of pushing a pencil a little simpler, unless you need the practice of course http://www.wolframalpha.com/input/?i=%288-x%29%28-14-x%29%283%2B9i-x%29%283-9i-x%29

amistre64 · Answer

3+9i-x
3-9i-x
--------
9+27i-3x
   -27i      +81+9i x
         -3x        -9i x  +x^2
------------------------
9       -6x  +81         +x^2


x^2 -6x +90   multiply that by the first one you found

anonymous · Answer

Thank you so much!

amistre64 · Answer

youre welcome