Question

find a second degree polynomial with zeros 2 + or - i

Answer 1

Multiply this out: \[
(x-(2-i))(x-(2+i))
\]

Answer 2

Since we know \(f(x) = (x-root_1)(x-root_2)\)

Answer 3

okay so is that what i have to do for each equation that says that?

Answer 4

a number is called algebraic when it is the root of a polynomial with integer coeffficients . show that the square root of 5 is algebraic. (hint if square root of 5 is algebraic then it is the root of polynomial with integer coefficients. find a second degree polynomial wiht integer coefficients and +square root 5 at its roots. the complete factorization theorem might be useful here)