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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

Hi badiuddin the above question is from AIST FIITJEE there they gave the answer of this question as 3/4,1 and 5/4.....but they don't give the detail solution.....and u gave the ans only 5/4....

11 years ago

11 years ago

**Dear Tapasranjan**

**I have given the range of a for which given equation has real solution **

**3/4 ≤ a ≤ 5/4 **

**for exactly 3 solution ,**

**1) any equation has 1 root and the other equation has 2 root then 3 solution are possible .**

**2) Or both the equation has 2 roots , but one root in both the equation is common then also exactly 3 solution is possible .**

** 1st case is possible at end point of the calculated range of a ie a=3/4 and 5/4 (because at this point discrimnent of one equation is zero already derived in earlier post )**

**and for the second case**

**formed two equation x^{2} -3x+a+1 =0 for x≥a**

** x^{2} -x+1-a =0 for x<a **

**let β is a common root**

**then it is satisfied by both the equation **

** **

** **β** ^{2} -3**β

** **β** ^{2} -**β

**solve **for β

**β =a **

**put this value of in any one of the equation **

**a^{2} -a+1-a =0**

**(a-1) ^{2} =0**

**a =1 **

**so for a=1 also exactly 3 solution exicts**

^{Please feel free to post as many doubts on our discussion forum as you can.If you find any question Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.All the best. Regards,Askiitians ExpertsBadiuddin}

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