Question

Please help in
Question number 4

Answer 1

here is your required answer

Answer 2

Hey, here's your answer ..................

Given that it has equal roots.............

(1+m²)x²+2mcx+(c²-a²)=0.........

R. T. P: c²=a²(1+m²)

Proof : We know discriminant Δ=0,when it has equal roots.
So, here .........
a=(1+m²); b=2c ; c = c²- a² ............
So (Δ)b²-4ac =0

Substituting the values ...............

(2c) ² - 4(1+m²)(c²- a²)=0...............

4c² - (4+4m²)(c²-a²) =0............
4c² - (4c²- 4a² + 4c²m²- 4m²a²) =0

4c²-4c² + 4a² - 4c²m² + 4m²a² =0

4 (a²-c²m² + m²a²) = 0

Hence, a² - c²m² + m²a²=0

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