If the equation (1+m2)x2+2mcx+(c2-a2)=0 has . . .

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

Doubt by Aditi 

Solution : 

(1+m²)x²+2mcx+(c²-a²)=0

Here
A = (1+m²)
B = 2mc
C = (c²-a²)

D = B²-4AC

0 = (2mc)²-4(1+m²)(c²-a²)
[∵Roots are equal so D=0]
0 = 4(mc)²-4(1+m²)(c²-a²)
0 = 4m²c²-4[1(c²-a²)+m²(c²-a²)]
0 = 4[m²c²-c²+a²-m²c²+m²a²]
0/4 = -c²+a²+m²a²
0 = -c²+a²+m²a²
c² = a²+m²a²
c² = a²(1+m²)

Hence Proved.