let a, b and c are unequal real positive numbers such that 2b = a + c, then roots of ax^2 + 2bx + c = 0 are


(i) real and equal (ii) Real and distinct (iii) imaginary (iv) nothing definite can be said


Plz explain

3 years ago

Share

Answers : (3)

                                        

Dear student,


2b=a+c


Sum of the roots=-2b/a


Product=c/a


This shows the roots are real and distinct...








Please feel free to ask your queries here. We are all IITians and here to help you in your IIT JEE preparation.


All the best.


Win exciting gifts by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.


Now you score 5+15 POINTS by uploading your Pic and Downloading the Askiitians Toolbar  respectively : Click here to download the toolbar..


 


Askiitians Expert


Sagar Singh


B.Tech, IIT Delhi


sagarsingh24.iitd@gmail.com







3 years ago
                                        

for any quadratic eq  ax2+bx+c roots are given by


 X = {-b+_ D)/2a


D =discriminant = (b2-4ac)1/2


our eq is ax2+2bx+c so


D = {(2b)2-4ac)1/2 ........1


2b = a+c  (given)


so , (2b)2 = (a+c)2 ...........2


putting  eq2 in eq1


D = { (a+c)2 - 4ac}1/2  =  { a2+c2-2ac}1/2 ={(a-c)2}1/2 =a-c


now roots are


 X = (-2b +_ D}/2a = {-2b + (a-c)}/2a     or        {-2b-(a-c)}/2a                                   


                           = -c/a                      or        -1                                  (on putting 2b =a+c )


so the roots are unequal & real


option (ii) is correct

3 years ago
                                        

the equation is ax^2+2bx+c=0


the discriminant is= B^2-4AC


A=a,B=2b,C=c


discriminant= 4b^2-4ac


but 2b=a+c, therefore (2b)^2=(a+c)^2


= (a+c)^2-4ac


=a^2+c^2+2ac-4ac


=a^2+c^2-2ac


=(a-c)^2, which is always greater than zero


therefore roots are real and distinct

3 years ago

Post Your Answer

More Questions On IIT JEE Entrance Exam

Ask Experts

Have any Question? Ask Experts
Post Question
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details
sir, pl. help me to solve following problems of permutation & combination- Q1. how many divisors of 9000 are even but not divisible by 4?also find the sum of such nos. Q2. the no. of ways an...
 
 
[Q-1]9000=3 2 5 3 2 3 we have to take exactly one 2. so number of ways (2+1)(3+1)(1)= 12 Sum of such numbers =(2)(3 0 + 3 1 +3 2 )(5 0 +5 1 +5 2 +5 3 ) [Q-2] first of all give 2 marks to...
  img
Nishant Vora one month ago
I’ve dropped after 12 th after I was unable to Qualify for 1 st attempt in JEE-Advanced (because of New Pattern I have not cleared the cut-off for JEE-Advanced). Second time I was unable to...
 
 
You cannot appear as fresher as for JEE as you have already appeared twice for JEE. As far as your dream of doing research in IIT, you can still achieve that dream. For now you can take...
  img
Aziz Alam 3 months ago
 
Thanks AZIZ :) This is a great suggestion for me Dear...but It’s better to remove doubts at all..haina So I am on your advice to take admission in some Good College... Actually the Problem...
 
HImanshu 2 months ago
 
Hey Himanshu, Getting into MIT or other good foreign university require good SAT score plus a strong academic background. Usually strong background means good scores in school level exams...
 
Rakesh Singh 2 months ago
RIGHT NOW I AM IN CLASS 12 th AND I WANT TO KNOW THAT CAN I APPER FOR IIT ENTRANCE EXAM AFTER 2 YEARS OF PASSING MY 12TH CLASS AND RIGHT NOW MY AGE IS 16+9 PLZ SOME ONE RPLY
 
 
Hi, You can sit fior JEE Advanced only in the year your are giving your 12 th board exams, and the year immediately next to it. So you cant appear for the exam after 2 years....
  img
Yash Baheti one month ago
 
what if i dont give the exam immediately after passing 12 , and after having some coaching after 12 for to years
 
nikhil pawar 29 days ago
View all Questions »