Question

Form the polynomial equation with rational coefficient and whose roots are 1+-2i 4,2

Answer 1

Answer:

Factor = Root

Make sure you aren’t confused by the terminology. All of these are the same:

Solving a polynomial equation p(x) = 0

Finding roots of a polynomial equation p(x) = 0

Finding zeroes of a polynomial function p(x)

Factoring a polynomial function p(x)

There’s a factor for every root, and vice versa. (x−r) is a factor if and only if r is a root. This is the Factor Theorem: finding the roots or finding the factors is essentially the same thing. (The main difference is how you treat a constant factor.)