p(x)=[tex]x^{4}[/tex] - [tex]98x^{2}[/tex] + 800x - 1599
given x = a is a zero of a polynomial p (x) then
(x - a) is a factor of the polynomial
complex zeros occur in conjugate pairs
5 + 4i is a zero hence 5 - 4i is a zero
factors are (x - 3),(x + 13),(x - (5 + 4i) and (x - (5 - 4i)
The polynomial is the product of it's factors
p(x) = (x - 3)(x + 13)(x - (5 + 4i)(x - (5 - 4i)
expanding the factors
p(x) = ([tex]x^{2}[/tex] + 10x - 39)([tex]x^{2}[/tex] - 10x + 41)
= [tex]x^{4}[/tex] - [tex]98x^{2}[/tex] + 800x - 1599
