Question 119662
If 2-4i is a root, then when {{{x=2-4i}}}, the entire left side will equal zero.


{{{x^2-4x+4a=0}}} Start with the given equation



{{{(2-4i)^2-4(2-4i)+4a=0}}} Plug in {{{x=2-4i}}}



{{{4-16i+16i^2-8+16i+4a=0}}} Foil and distribute



{{{4-16i+16(-1)-8+16i+4a=0}}} Replace {{{i^2}}} with {{{-1}}}



{{{4-16i-16-8+16i+4a=0}}} Multiply


{{{4a-20=0}}} Combine like terms





{{{4a=0+20}}}Add 20 to both sides



{{{4a=20}}} Combine like terms on the right side



{{{a=(20)/(4)}}} 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