Question

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

Answer 1

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Answer 2

Solution:

Given Quadratic equation :

(1+m²)x²+2mcx+(c²-a²)=0

Compare above equation with

Ax²+Bx+C=0 ,we get

A=(1+m²), B = 2mc, C = (c²-a²)

Discreminant (D) = 0

=> B²-4AC = 0 /* Given roots are equal */

=> (2mc)²-4(1+m²)(c²-a²)=0

=> 4m²c²-4(c²-a²+m²c²-m²a²)=0

=> 4[m²c²-(c²-a²+m²c²-m²a²)]=0

=> m²c²-c²+a²-m²c²+m²a² =0

=> -c²+a²+m²a²=0

=> a²(1+m²) = c²

Therefore,

c² = a²(1+m²)

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