Q1: If k is a root of a polynomial, then the polynomial is a multiple of (x-k).
So, given the roots 0. -2 and 7, the polynomial must be at least
[tex](x-0)(x-(-2))(x-7)=x(x+2)(x-7)[/tex]
Q2: If a polynomial with real coefficient has a complex root z, then its conjugate z' must be a solution as well.
So, if 5-i is a root, its conjugate 5+i must be a root as well.
