Question

If the equation (l + m^2)x^2 + 2mcx + (c^2 - a^2) = 0 has equal roots, help me to prove that c^2= a^2(l + m^2)..

Answer 1

★ QUADRATICS RESOLUTION ★

☣ CONDITIONS IMPLEMENTED → FOR EQUAL ROOTS

☣ HENCE , D=0 , b² = 4ac

☣ PROCEEDING IN THAT MANNER ...

☣ GIVEN EQUATION ...

☣ (1 + m²)x² + 2mcx + ( c² - a² ) =0

☣ FOR EQUAL ROOTS ...

☣ 4m²c² = 4( 1 + m² ) ( c² - a² )

☣ 4m²c² = 4c² - 4a² + 4c²m² - 4a²m²

☣ 4c² - 4a²m² - 4a² = 0

☣ 4 [ c² - a²m² - a² ] = 0

☣ c² = a²m² + a²

☣ c² = a² [ 1 + m² ]

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