if the equation (1+m^2)x^2 +2mcx +(c^2-a^2)=0 have equal roots prove that c^2=a^2 (1+m^2)
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D=0.(equation has equal roots)
so b^2-4ac=0
(2mc)^2-4(1+m^2)(c^2-a^2)=0
4m^2c^2-4(c^2-a^2+m^2c^2-m^2a^2)=0
4m^2c^2=4(c^2-a^2+m^2c^2-m^2a^2)=0
c^2-a^2-m^2a^2=0
c^2=a^2(1+m^2)
so b^2-4ac=0
(2mc)^2-4(1+m^2)(c^2-a^2)=0
4m^2c^2-4(c^2-a^2+m^2c^2-m^2a^2)=0
4m^2c^2=4(c^2-a^2+m^2c^2-m^2a^2)=0
c^2-a^2-m^2a^2=0
c^2=a^2(1+m^2)
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