Question

Find the discriminant of x^2 - 4ax + 4a^2 - 4b^2

Answer 1

given, quadratic equation,

x^2 - 4 a x +( 4 a^2 - 4 b ^2 )

here, a = 1 , b = - 4a , c = 4 a^2 - 4 b^2
as we know,
discriminant (D) = b^2 - 4 a c

D = b^2 - 4ac
= (- 4 )^2 - 4( 1 )( 4 a^2- 4 b^2 )

D = 16 - 16 a^2 + 16 b ^2

D = -16 a^2 + 16 b^2 + 16

D = -16 (a^2 - b^2 - 1 )

D = -16 {( a - b ) (a + b ) - 1 }

★hope it helps★