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Tapasranjan Das Grade: 12
        

Q: The value of 'a' for which the equation (x-1)2=|x-a| has exactly three real solutions is/are


A. 1/4


B. 3/4


C. 1


D. 5/4

7 years ago

Answers : (1)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear Tapasranjan


(x-1)2=|x-a|


case: x≥a


 (x-1)2=(x-a)


x2 +1 -2x =x-a


x2  -3x+a+1 =0


 x = [3 ±√9-4(a+1)]/2


 for real value of x


9-4(a+1)≥0


5/4 ≥a


 


 case: x<a


(x-1)2=-(x-a)


x2 +1 -2x =-x+a


x2  -x+1-a =0


 x = [1 ±√1-4(1-a)]/2


 for real value of x


1-4(1-a)≥0


a≥3/4


for exactly 3 value  in any one case discrimnent must be zero


so either a =3/4 or a =5/4


 but for a=3/4 both case give only single value


so solution is 5/4


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Badiuddin

7 years ago
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