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pallavi pradeep bhardwaj Grade: 12
        

The number of quadratic equation which are unchanged by squaring their roots is

7 years ago

Answers : (3)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear pallavi


let x2 +bx +c=0 ............1


not let another equation whoose roots are square of this equation


so   X=x2   or   x=√X


 put value of x


  X +b√X  +c =0


 or X +c =-b√X


square


   X2 +c2 +2cX =b2X


   X2 +(2c-b2)X + c2 =0..................2


root of equation 2 is the square of root of equation 1


both equation will be same if their coefficient are in proportion


1/1  =b/(2c-b2)  =c/c 2


b= 2c-b2     ................3            


c=c2  ....................3


 from equation 3  c=0 or 1


 for c =0  b= 0 and -1


  for c=1  b= 1 and -2 


So, four combination are possible


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Badiuddin

7 years ago
Jay Lal
14 Points
										

There are four such cases x=0 root 0


(x-1)2=0  root 1


x(x+1)=0  roots  0 and 1


x2+x+1=0 roots ω and ω2 

5 years ago
Panchin Ganeriwal
34 Points
										The four roots are:

Equations             roots
x2 = 0                       0,0
x (x-1)=0.                 1,0
(x-1)2 = 0.                1,1
x2+x+1=0              ω  ω2
I think u all must have found out the first three equarions , but the challenge was the fourth one
one year ago
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