Question

If the quadratic equation (1 + m square ) x square plus 2 m c x + c square minus a square equals to zero has equal roots prove that c square equals to a square (1+msquare)

Answer 1

Step-by-step explanation:

(1 + m2)x2 + 2 mcx + c2 - a2 = 0 has equal roots ⇒ b2 - 4ac = 0 ⇒ (2 mc)2 - 4(1 + m2)(c2 - a2) = 0 ⇒ 4m2c2 - 4(c2 - a2 + m2c2 - m2a2) = 0 ⇒ 4m2c2 - 4c2 + 4a2 - 4m2c2 + 4m2a2 = 0 ⇒ 4m2a2 - 4c2 + 4a2 = 0 ⇒ m2a2 - c2 + a2 = 0 ⇒ a2(1 + m2) - c2 = 0 ⇒ c2 = a2(1 + m2) Hence proved.