Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 550 off


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....

6 years ago


Answers : (2)


This Q can be solved by opening the modulus sign with + and - signs, one at a time. In this case you get a max. of 4 roots, two for each + and - signs. For getting exactly 3 roots, following may be the cases,
a) One of the equations (modulus with + or - sign) has both equal roots, and the other 1
has two distinct roots.
b) Both + and - give you distinct roots, but 1 root of + and 1 root of - become same.
Now when opened with '+' : a1= 1, b1=3 and c1=(1+a). Solving b1^2-4a1c1=0, we get a =5/4.
Similarly for opening with '-' sign: a2=1, b2= -1, c2=(1-a). Solving this you get a=3/4.

Now there can be the last possibility: Put both b1^2 - 4a1c1 > 0 and b2^2 - 4a2c2 > 0.
You get: a< 5/4 and a > 3/4, which gives you the last value, that is 1.
So you get your final answer as:a = 3/4, 1, 5/4.
Please always specify, whether the Q has single or multiple correct option, as you are specified in the exam, it is incomplete otherwise, as a Q is left after we get a value and nothing is mentioned to proceed after that.
Thank you
6 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 x2  -3x+a+1 =0   for x≥a

                              x2  -x+1-a =0     for x<a 

let β is a common root

then it is satisfied by both the equation


   β2  -3β+a+1 =0

   β2  -β+1-a =0

solve for β  

β =a

put this value of in any one of the equation

a2  -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.
Askiitians Experts

6 years ago

Post Your Answer

Other Related Questions on Algebra

Given the three circles x 2 +y 2 -16x+60=0, 3x 2 +3y 2 -36x+81=0,x 2 +y 2 -16x-12y+84=0,find (i)the point from which the tangents to them are equal in length and (ii)this length.
let that point be (h.k) Now we know that Length of tangent is given by root(S1) So length of tangent to circle 1 is root(h2+k2-16h+60) Similarily for other two and then equate all the...
Nishant Vora one month ago
The radical axis of two circles has the property that the tangents drawn from a point on it to both the circles will have the same length. Radical axis equation quite naturally is S 1 =S 2...
mycroft holmes one month ago
Can you plz explain it clearly to me to understand?? thanking you Sir..............................................................................................................
Hansraj Gyanendra Singh Rajawat one month ago
FIND DOMAIN:- 1.sqrt cos(sinx) 2.sqrt sin(cosx) 3.1/sqrt 1+2sinx
For finding out the domain of the sqrt function, is should only take care of the condition that anything inside the sqrt should be always greater then or equal to positive only. It...
Vijay Mukati 3 months ago
0 to 2pi ,,,,pi/2 to -pi/2 these are the answers to the first two questions... similarly solve the third question and obtain the domain. always remember that denominator not equal to zero...
Rishabh Ranjan Das 3 months ago
there is a question from complex no. mam please help me for getting its answer
Kindly submit the desired question for the experts to answer! Two complex numbers are equal if and only if both their real and imaginary parts are equal. In symbols: {\displaystyle...
Stan one month ago
Find domain and range and describe nature of graph sir
It will be great if u can specifically pick example so that i can explain in better way. In general u draw vertical linealonggraph, itwill represent range where horizontal line paralle to x...
Harsh Patodia one month ago
what is the applications of matrices in daily life?
NARAYANA 10 months ago
This is to inform all forum users who are posting questions and then approving answers of all the users in same question just to give points to their friends so that they can get the gift...
Forum Team 9 months ago
Hello Kumar In mathematics , a matrix (plural matrices ) is a rectangular array—of numbers, symbols, or expressions, arranged in rows and columns—that is treated in certain prescribed ways. ...
Gaddam Chethan 10 months ago
Write direction ratios of the vector a = i + j − 2k and hence calculate its direction cosines?
Note that direction ratios a, b, c of a vector r = x i + yj + zk are just the respective components c, y and z of the vector. So, for the given vector, we have a = 1, b=1, c= –2. Further,...
KUNCHAM SAMPATH 10 months ago
View all Questions »

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 3,750 off

Get extra R 550 off

More Questions On Algebra

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details