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`        The number of quadratic equation which are unchanged by squaring their roots is`
7 years ago

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
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  & AIEEE preparation.
```
7 years ago
Jay Lal
14 Points
```										There are four such cases x2  =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             rootsx2 = 0                       0,0x (x-1)=0.                 1,0(x-1)2 = 0.                1,1 x2+x+1=0              ω  ω2I 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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