SOLUTION: One root of x^2-4x+4a=0 is 2-4i. What is the value of a ?

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Question 119662: One root of x^2-4x+4a=0 is 2-4i. What is the value of a ?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If 2-4i is a root, then when x=2-4i, the entire left side will equal zero.

x%5E2-4x%2B4a=0 Start with the given equation


%282-4i%29%5E2-4%282-4i%29%2B4a=0 Plug in x=2-4i


4-16i%2B16i%5E2-8%2B16i%2B4a=0 Foil and distribute


4-16i%2B16%28-1%29-8%2B16i%2B4a=0 Replace i%5E2 with -1


4-16i-16-8%2B16i%2B4a=0 Multiply

4a-20=0 Combine like terms




4a=0%2B20Add 20 to both sides


4a=20 Combine like terms on the right side


a=%2820%29%2F%284%29 Divide both sides by 4 to isolate a



a=5 Divide

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Answer:
So our answer is a=5



Note: you can check this answer by using the quadratic formula