SOLUTION: Find a third-degree polynomial equation with rational coefficients that has roots –4 and 6 + i.

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Find a third-degree polynomial equation with rational coefficients that has roots –4 and 6 + i.       Log On


   

Question 674271: Find a third-degree polynomial equation with rational coefficients that has roots –4 and 6 + i.
Answer by ReadingBoosters(3246) About Me  (Show Source):
You can put this solution on YOUR website!
Given roots
-4 and 6+i
Inferred root 6-i (conjugate pair of 6+i)
...
x = -4
x + 4 = 0
(x+4)
...
x = 6 + i
x - 6 = sqrt%28-1%29
%28x-6%29%5E2+=+-1
%28x-6%29%5E2+%2B+1+=+0%0D%0A...%0D%0A%7B%7B%7B%28x%2B4%29%28x-6%29%5E2+%2B+1+=+0
%28x%2B4%29%28x%5E2-12x%2B36%29+%2B+1+=+0
...
x%5E3+-+12x%5E2+%2B+36x+%2B+4x%5E2+-+48x+%2B+144+%2B1+=+0
...
highlight_green%28x%5E3+-+8x%5E2+-+12x+%2B+145=0%29
.....................
Delighted to help.
-Reading Boosters
Website: www.MyHomeworkAnswers.com
Wanting for others what we want for ourselves.