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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