Q. 135.0( 12 Votes )

If the equation (

Answer :

The given equation is : (1 + m2)x2 + 2mcx + c2 - a2 = 0


Roots of an equation are given by the formula:


x = , where, D = b2 – 4ac


For equal roots, D = 0


On comparing with ax2 + bx + c = 0, we get:


a = 1 + m2, b = 2mc, c = c2 - a2


Therefore, D = 0


(2mc)2 – 4(1 + m2)(c2 - a2) = 0


4m2c2 – 4c2 + 4a2 – 4m2c2 + 4m2a2 = 0


- 4c2 + 4a2 + 4m2a2 = 0


4c2 = 4a2 + 4m2a2


4c2 = 4a2 (1 + m2)


c2 = a2 (1 + m2)


Hence, proved.


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