Question

If the equation (l+m^2)x^2+2mcx+c^2-a^2=has equal roots then show that c^2=a^2(1+m^2).

Answer 1

let roots are α ,α

2α = -2mc/(l+m^2)

α^2 = - a^2/(l+m^2)

substituting α in a^2

(-mc/{l+ m^2})^2 = -a^2/(1+m^2)

m^2*c^2 = -a^2*(1+m^2)

c^2 = -a^2(1+m^2)/m^2