Question

a polynomial functiion P(x) with rational coefficients has the given roots. find two additional roots of p(x)=0

2i and √ 10

Answer 1

If -2i is a root, then 2i is also a root. If √10 is a root, then -√10 is also a root. Convert all four of these roots into factors using the factor theorem (which says that if R is a root, then (x - R) is a factor). (x + 2i) (x - 2i) (x - √10) (x + √10) Multiply these factors together. (It's easiest to multiply the conjugate pairs together first.): x^4 - 6x^2 - 40