SOLUTION: Help please. I understand how to get the answers from quadratic equations. My problem is writing a quadratic equation from the solutions: 3+4i, 3-4i. This has me stumped.

Click here to see ALL problems on Quadratic Equations

Question 320461: Help please. I understand how to get the answers from quadratic equations. My problem is writing a quadratic equation from the solutions: 3+4i, 3-4i. This has me stumped.
Found 2 solutions by ankor@dixie-net.com, CharlesG2:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
My problem is writing a quadratic equation from the solutions: 3+4i, 3-4i.
:
x = 3 +/- 4i
subtract 3 from both sides
x - 3 = +/- 4i
Square both sided
(x - 3)^2 = 16i^2
FOIL
x^2 - 3x - 3x + 9 = 16(-1)
:
x^2 - 6x + 9 = -16
:
x^2 - 6x + 9 + 16 = 0
:
x^2 - 6x + 25 = 0; is the equation

Answer by CharlesG2(834) (Show Source):
You can put this solution on YOUR website!
"Help please. I understand how to get the answers from quadratic equations. My problem is writing a quadratic equation from the solutions: 3+4i, 3-4i. This has me stumped."
---
Quadratic Equation: ax^2 + bx + c = 0
---
if solution is 3+4i:
3 + 4i - (3 + 4i) = 0
3 + 4i - 3 - 4i = 0
let's call this x - (3 + 4i) = 0
---
if solution is 3-4i:
3 - 4i - (3 - 4i) = 0
3 - 4i - 3 + 4i = 0
let's call this x - (3 - 4i) = 0
---
so then we have:
(x - (3 + 4i))(x - (3 - 4i)) = 0
we need to multiply this out using FOIL to get our quadratic equation
---
x * x + x * -(3 - 4i) + x * -(3 + 4i) + (3 + 4i)(3 - 4i) = 0
x^2 + x * (4i - 3) + x * (-4i - 3) + 9 - 16i^2 = 0
x^2 + 4ix - 3x - 4ix - 3x + 9 + 16 = 0 (i^2 = -1)
x^2 - 6x + 25 = 0 (and this is your quadratic equation)