SOLUTION: If the equation (1+m^2)x^2+2mcx+(c^2-a^2)=0has equal root ,prove that c^2=a^2(1+m^2)

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Question 631573: If the equation (1+m^2)x^2+2mcx+(c^2-a^2)=0has equal root ,prove that c^2=a^2(1+m^2)
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
(1+m^2)x^2+2mcx+(c^2-a^2)=0
Since the quadratic equation has equal roots the discriminant
b%5E2-4ac=0
where a=+%281%2Bm%5E2%29 , b= 2mc , c=%28c%5E2-a%5E2%29
%282mc%29%5E2-+4%281%2Bm%5E2%29%28c%5E2-a%5E2%29=0
4m%5E2c%5E2+-+4%28c%5E2-a%5E2%2Bm%5E2c%5E2-m%5E2a%5E2%29=0
4m%5E2c%5E2+-+4c%5E2%2B4a%5E2-4m%5E2c%5E2%2B4m%5E2a%5E2%29=0
-4c%5E2%2B4a%5E2%2B4m%5E2a%5E2=0
4c%5E2=+4a%5E2%2B4a%5E2m%5E2
divide by 4
c%5E2=a%5E2%2Ba%5E2m%5E2
c%5E2=a%5E2%281%2Bm%5E2%29
m.ananth@hotmail.ca