1.

If the quadratic equation (1 + m2)x2 + 2 mcx + c2 - a2 = 0 has equal roots, prove that c2 = a2 (1 + m2).

Answer»

D=b^2-4ac=0
(2MC)^2-4(1+m^2)(c^2-a^2)=0
4m^2c^2-4(c^2+m^2c^2-a^2-a^2m^2)=0
4m^2c^2-4c^2-4m^2c^2+4a^2+4m^2a^2=0
-4c^2+4a^2+4m^2a^2=0
-c^2+a^2+m^2a^2=0
-c^2+a^2(1+m^2)=0
C^2=a^2(1+m^2)


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