SOLUTION: (2m+1)x^2 -4mx = 1-3m, has equal roots. Find the roots.

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Question 1199688: (2m+1)x^2 -4mx = 1-3m, has equal roots. Find the roots.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
%282m%2B1%29x%5E2-4mx%2B3m-1=0

%282m%2B1%29x%5E2-4mx%2B%283m-1%29=0

If you can think of nothing else, use general solution formula for quadratic equation, and just perform the needed algebra steps. Be aware if you expect the roots to be equal, then discriminant is 0.

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discriminant, %28-4m%29%5E2-4%2A%282m%2B1%29%283m-1%29
16m%5E2-4%286m%5E2%2Bm-1%29
16m%5E2-24m%5E2-4m%2B4
-8m%5E2-4m%2B4 which needs to be 0.
8m%5E2%2B4m-4=0
2m%5E2%2Bm-1=0
Factor?
%282m-1%29%28m%2B1%29=0
Either m=1%2F2 or m=-1
You should recheck each to see if they both work.