If the equation 
has equal roots, prove that 
.
For a quadratic equation, ax2 + bx + c = 0,
D = b2 – 4ac
If D = 0, roots are equal
⇒ D = 4m2c2 – 4(c2 – a2)(1 + m2) = 0
⇒ m2c2 – c2 + a2 – c2m2 + a2m2 = 0
⇒ c2 = a2(1 + m2)
15
If the equation has equal roots, prove that .
For a quadratic equation, ax2 + bx + c = 0,
D = b2 – 4ac
If D = 0, roots are equal
⇒ D = 4m2c2 – 4(c2 – a2)(1 + m2) = 0
⇒ m2c2 – c2 + a2 – c2m2 + a2m2 = 0
⇒ c2 = a2(1 + m2)