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

147 Points
11 years ago

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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Jay Lal
14 Points
8 years ago

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

Panchin Ganeriwal
34 Points
4 years ago
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