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CBSE Class 11-science Answered

For space what space values space of space straight a comma space the space roots space of space thwe space equation space 2 straight x squared minus left parenthesis straight a plus 1 right parenthesis straight x plus left parenthesis straight a minus 1 right parenthesis equals 0
is space equal space to space their space product ?
Asked by aahnik.mohanty | 10 Jun, 2019, 08:24: PM
answered-by-expert Expert Answer
The question should be like this
For what values of a the difference of roots of the equation 2x- (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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