Question

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

Answer 1

Hi dear !!


here is your answer !!

since root are equal so

D = 0

so b² -4ac = 0


for full solution look this attachment :-


hope it help you dear !!!

thanks !!!

Answer 2

Solution :

Compare given Quadratic equation

(1+m²)x²+2mcx+c²-a²=0 with

Ax² + Bx + C = 0 ,we get

A = 1+m² ,

B = 2mc ,

C = c²-a² ,

Now ,

Discreminant (D) = 0 [ equal roots ]

B² - 4AC = 0

=> ( 2mc )² - 4×(1+m²)(c²-a²) = 0

=> 4m²c²-4(c²-a²+m²c²-a²m² )= 0

=> 4m²c² - 4c² + 4a² - 4m²c² + 4a²m² = 0

=> -4c² + 4a² + 4a²m² = 0

Divide each term by 4 , we get

=> -c² + a² + a²m² = 0

=> -c² + a²( 1 + m² ) = 0

=> a²( 1 + m² ) = c²

Therefore ,

c² = a²( 1 + m² )

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