Question

Determine the nature of the roots of the following quadratic equations:
(i) (x – 2a) (x − 2b) = 4ab
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Answer 1

Answer:

x^2 - 2xb - 2xa + 4ab = 4ab

x^2 - 2x(a+b) + 4ab -4ab = 0

x^2 - 2x(a+b) + 0 =0

compare this with the general form of quadratic eq. i.e. Ax^2 + Bx + C =0

A=1 & B=-2(a+b) and c=0

D = b^2 + 4ac

={-2(a+b)^2} - 4 × 1 × 0

= {4( a^2 + b^2 + 2ab)}

= (4a^2 + 4b^2 + 4ab) = *( a^2 + b^2 + 2ab) = (a + b)^2

Hence D is greater than 0

real root exits.