Quadratic equations

Asked by abhishek11 | 25th May, 2010, 07:11: PM

Expert Answer:

(x-a)(x-b) = c

x2 -(a+b) + ab = c

x2 -(a+b) + ab - c = 0

α + β = a + b and αβ = ab - c           ... (1)

Now, (x - α)(x - β) + c = a

x2 -(α + β)x + αβ + c = a

Substituting from (1),

x2 -(a + b)x + ab - c + c = a

x2 -(a + b)x + ab - a = 0

The roots are,

= {(a+b)±[(a+b)2 - 4a(b-1)]}/2

= {(a+b)±[(a-b)2+4a)]}/2

Regards,

Team,

TopperLearning.

 

Answered by  | 26th May, 2010, 12:18: PM

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