For a
polynomial with real cofieints, if a+bi is a root, a-bi is also a
root
zeros,
i and 5-i
passes
through origin means 0 is also a zero
get
plus and minus of the roots
i,
-1, 5-i, 5+i and 0 are roots
for a
poly with roots, r1,r2,r3,r4,r5, the facotred form is
(x-r1)(x-r2)(x-r3)(x-r4)(x-r5)
sub
the roots
(x-i)(x-(-i))(x-(5-i))(x-(5+i))(x-0)=
(x-i)(x+i)(x-5+i))(x-5-i))(x)=
x(x^2+1)(x^2-10x+26)=
x^5-10x^4+27x^3-10x^2+26x
the
polynomial is f(x)=x^5-10x^4+27x^3-10x^2+26x
