Question 1052703
with zeros of 0 and 8, the factors are x and (x-8)
1+/-sqrt2i needs to be found.
[-b +/- sqrt (b^2-4ac)](1/2) needs to be evaluated
if a is 1 and b is -2, x=(1/2)(2 +/- sqrt (4-4(1)(c))
This gives me 1 +/- sqrt (4-4c), and that has to become negative 16, because then it will be 4i, and it is divided by 2 in the formula, and that will be 2i.
c has to be 5, then sqrt (4-4c)=sqrt(-16)
The third factor is (x^2-2x+5), and x=(1/2)+/- (2 +/- sqrt (4-20))
=(1/2)(2+/-4i)=1+/-2i

The polynomial is x(x-8)(x^2-2x+5)=x^4-10x^3+21x^2-40x.
{{{graph(300,300,-10,10,-400,100,x^4-10x^3+21x^2-40x)}}}