Q1 of 227 Page 110

Determine the nature of the roots of the equation.

(x – 2a) (x – 2b) = 4ab

(x – 2a)(x – 2b) = 4ab


⇒ x(x –2b) – 2a(x – 2b) = 4ab


⇒ x2 – 2bx – 2ax + 4ab – 4ab = 0


⇒ x2 – 2x(b + a) = 0



⇒ a = 1, b = –b – a and c = 0


= (–b – a )2– 4(1)(0)


b2 + a2 + 2ab


∴ b2 – 4ac > 0. hence, roots are real.


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