SOLUTION: what is is polynomial function of least degree with real coefficients -4, 2i, and -2i?

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: what is is polynomial function of least degree with real coefficients -4, 2i, and -2i?      Log On


   

Question 785719: what is is polynomial function of least degree with real coefficients -4, 2i, and -2i?
Answer by fcabanski(1391) About Me  (Show Source):
You can put this solution on YOUR website!
This problem is not written correctly. The given values are zeroes instead of coefficients. Not all of them are real.


To find a polynomial of least degree with the roots -4, 2i and -2i, subtract the zeroes from x to find factors.


x=-4 ---> x+4


x=2i --->x-2i


x=-2i ---> x+2i


Multiply the factors together. It's wise to multiply the factors involving imaginary numbers together first.


(x-2i)(x+2i) = x%5E2+-4i%5E2 and since i=sqrt%28-1%29 that's x%5E2+%2B4.


%28x%2B4%29%28x%5E2+%2B+4%29+=+x%5E3+%2B+4x%5E2++%2B4x+%2B+16


Since some number, a, may have been factored out of each term, multiply the whole thing by a. a%28x%5E3+%2B+4x%5E2++%2B4x+%2B+16%29