SOLUTION: Hi. I am having trouble with this question: Which equation, in axsquared + bx + c form, has the roots 5

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Question 205026: Hi.
I am having trouble with this question:
Which equation, in axsquared + bx + c form, has the roots 5 - 2i and 5 + 2i. thanks.

Found 2 solutions by ankor@dixie-net.com, scott8148:
Answer by ankor@dixie-net.com(22740) (Show Source):
You can put this solution on YOUR website!
Which equation, in axsquared + bx + c form, has the roots 5 - 2i and 5 + 2i.
:
x = 5 +/- 2i
Subtract 5 from both sides:
x - 5 = +/- (2i)
Square both sides
(x - 5)^2 = 4(i^2)
FOIL the left, i^2 = -1
x^2 - 10x + 25 = 4(-1)
:
x^2 - 10x + 25 = -4
:
x^2 - 10x + 25 + 4 = 0
:
x^2 - 10x + 29 = 0

Answer by scott8148(6628) (Show Source):
You can put this solution on YOUR website!
if R is a root, then (x - R) is a factor

(x - 5 + 2i)(x - 5 - 2i) = x^2 - 5x - 2ix - 5x + 25 + 10i + 2ix - 10i - 4i^2 = x^2 - 10x + 29

0 = x^2 - 10x + 29

SOLUTION: Hi. I am having trouble with this question: Which equation, in axsquared + bx + c form, has the roots 5 - 2i and 5 + 2i. thanks.