SOLUTION: Write the quadratic equation witha lead coefficient of 1 whose roots are 3+2i and 3-2i.
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Question 67379This question is from textbook Advanced mathematics
: Write the quadratic equation witha lead coefficient of 1 whose roots are 3+2i and 3-2i.
This question is from textbook Advanced mathematics
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Write the quadratic equation with a lead coefficient of 1 whose roots are 3+2i and 3-2i.
:
Sort of like completing the square backwards:
:
x = 3 +/-2i
:
Subtract 3 from both sides:
x - 3 = +/-2i
:
Square both sides:
(x-3)^2 = (+/-2i)^2
:
x^2 - 6x + 9 = 4(i^2)
x^2 - 6x + 9 = 4(-1)
x^2 - 6x + 9 = -4
:
Add 4 to both sides:
x^2 - 6x + 9 + 4 = 0
:
x^2 - 6x + 13 = 0 is the quadratic equation
:
You can check it by actually completing square on this equation
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