Question

A polynomial f(x) with real coefficients and leading coefficient 1 has zeros 2, -3 - 9i and degree 3. Express f(x) as a product of linear and quadratic polynomials with real coefficients that are irreducible over IR.

Answer 1

f(x) = (x-2)(x+3+9i)(x+3-9i)

Answer 2

then you can expand the last two

Answer 3

How do you foil it to remove the i's?

Answer 4

\[(a+z)(a+z conjugate ) \] = a^2 +a(z+z conj ) + z (z conj )

Answer 5

cant believe they dont have the bars on top :|

Answer 6

let a=x , z= 3+9i

Answer 7

x^2 + x ( 3+9i +3-9i) + (3+9i)(3-9i)

Answer 8

that should be it hopefully

Answer 9

(x^2 +6x + (9 - (-81) )

Answer 10

f(x) = (x-2)(x^2 +6x +90)

Answer 11

fair sure thats it

Answer 12

you can use quadratic formula to see if its correct.

Answer 13

see if that gives the two complex roots

Answer 14

and thats correct

Answer 15

Wow thanks heaps!