Question

find all the zeros and write a linear factorization of g(x)=x^4-8x^3+27x^2-50x+50 given that 1+2i is a zero

Answer 1

g(x)= (x-(1+2i)) * (x-(1-2i)) * (x-(3-i)) * (x-(3+i))

Please see attached image

Explanation:

We can easily solve this equation by using a technical solver or a programming language such as Octave.

The linear factorization of the equation can be obtained directly by finding the zeros of g(x)

Please see attached images for the answer to your problem

g(x)= (x-(1+2i)) * (x-(1-2i)) * (x-(3-i)) * (x-(3+i))