Question 1003892
Find a polynomial with real corfficients that has -2 and 2 + i as zeros
We have two factors from these zeros
x = -2
(x + 2) = 0
and
x = 2 + i
x - 2 = i
square both sides
(x-2)^2 = i^2
FOIL (x-2)(x-2); i^2 = -1
x^2 - 4x + 4 = -1
x^2 - 4x + 4 + 1 = 0
(x^2 - 4x + 5) = 0
Multiply these two factors
(x+2)(x^2 - 4x + 5)  = x^3 - 2x^2 - 3x + 10 is polynomial
:
:
looks like this
{{{ graph( 300, 200, -6, 5, -10, 14, x^3 - 2x^2 - 3x + 10) }}}