CBSE Class 11-science Answered
Asked by aahnik.mohanty | 10 Jun, 2019, 08:24: PM
Expert Answer
The question should be like this
For what values of a the difference of roots of the equation 2x2 - (a + 1)x + a - 1 = 0 is equal to their product.
The solution is
Let α and β are the roots of the given quadratic equation.
α + β = (a + 1)/2 and αβ = (a - 1)/2
(α - β)2 = (α + β)2 - 4αβ
(α - β)2 = (a + 1)2/4 - 2(a - 1)
(α - β)2 = (a - 3)2/4
α - β = ±(a - 3)/2
According to the question,
α - β = α β
(a - 3)/2 = (a - 1)/2
a - 3 = a - 1 which is not possible.
Hence, we consider α - β = -(a - 3)/2
α - β = α β
-(a - 3)/2 = (a - 1)/2
-a + 3 = a - 1
2a = 4
a = 2
Answered by Sneha shidid | 11 Jun, 2019, 10:35: AM
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