Question

If the equation (1+m^2)x^2 +2mcx + c^2 -a^2=0 has equal roots thwn Prove that
c^2 = a^2(1+m^2)​

Answer 1

Step-by-step explanation:

In the question given that it has equal roots so,

D = b² - 4ac = 0

Here,

a=1 + m²,

b = 2mc,

c = (c² -a²)

As,

(2mc)² - 4(1 + m²) (c² - a²) = 0

Now,

=> 4m²c² - 4(1 + m²) (c² - a²)

=> m²c² - (c² - a² + m²c² - m²a²) = 0

=> m²c² - c² + a² - m²c² + m²a² = 0

On solving,

=> - c² + a² + m²a² = 0

=> c² = a² + m²a²

Now taking a² as common,

=> c² = a² (1 + m²)

Hence proved