Question

please answer this question

Answer 1

Given Quadratic equation is

(1+m²)x²+2mcx+(c²+a²)=0

For a quadratic equation to have equal roots, discriminant Δ = 0

⇒B²=4AC (for a quadratic equation Ax²+Bx+C=0)

⇒(2mc)²=4*(1+m²)*(c²+a²)

⇒4m²c²=(4+4m²)*(c²+a²)

⇒4m²c²=4c²+4a²+4m²c²+4m²a²

⇒4(c²+a²+m²a²) = 0

⇒c²=-a²(1+m²)