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```        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```
7 years ago

SAGAR SINGH - IIT DELHI
879 Points
```										Dear student,
2b=a+c
Sum of the roots=-2b/a
Product=c/a
This shows the roots are real and distinct...

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.

Sagar Singh
B.Tech, IIT Delhi
sagarsingh24.iitd@gmail.com

```
7 years ago
510 Points
```										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
```
7 years ago
Fawz Naim
37 Points
```										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
```
7 years ago
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