Question

If the equation (1+m²)x²+2 mcx+(c²-a²)=0 has equal roots, prove that c² = a²(1 + m²).

Answer 1

SOLUTION :  

Given : (1 + m²)x² + 2 mcx + c² - a² = 0 has equal roots

On comparing the given equation with,  ax² +  bx + c = 0

Here, a =  (1 + m²) , b = 2mc , c =  c² - a²

Discriminant , D = b² -  4ac

D = 0 (has equal roots)

(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

4(m²a² - c² + a² ) = 0

m²a² - c² + a² = 0

a² + m²a² - c² = 0

a²(1 + m²) - c² = 0  

c²  = a²(1 + m²)

HOPE THIS ANSWER WILL HELP YOU...

Answer 2

okay wait I will solve... since having equal roots b2-4ac=0