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 !!!

since root are equal so .

D = 0

b² -4ac = 0

kindly look this attachment :-

for answer .

hope it help you !!!
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 ,

Discreminant ( D ) = 0

[ Since ,Given 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

After cancellation , we get

=> -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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