1.
Physics Helpline
L K Satapathy
Quadratic Equations 2

2.
Physics Helpline
L K Satapathy
Quadratic Equations 2
Answer :
Question : Let p and q be real numbers such that and
If  and  are non-zero complex numbers satisfying and
then a quadratic equation having and as its roots is
3 3
0 , .p p q p q   

 
     3 2 3 3
( ) 2 0a p q x p q x p q     
3 3
,p q       
     3 2 3 3
( ) 2 0b p q x p q x p q     
     3 2 3 3
( ) 5 2 0c p q x p q x p q           3 2 3 3
( ) 5 2 0d p q x p q x p q     
3 3
( ) ( )i p ii q       
3
3p p q   
   
3
3 q        
Given :
3
3
p q
p


 

3.
Physics Helpline
L K Satapathy
2
0x x
  
   
   
       
   
2 2
2
1 0x x
 

 
    
 
 2 2 2
0x x       
The quadratic equation having and as its roots is given by
 
2 2
( ) 2 0x x           

4.
Physics Helpline
L K Satapathy
Correct option = (b)
 33 3
2 2
2
0
3 3 3
p qp q p q
x p x
p p p
  
    
  
     3 2 3 3 3
3 2 0p q x p p q x p q         
     3 2 3 3
2 0p q x p q x p q      
Putting , we get
3
&
3
p q
p
p
  

   

5.
Physics Helpline
L K Satapathy
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