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Question

The number of quadratic equation(s), with real roots which remain unchanged even after squaring its roots, is 


Your Answer
A
1
Your Answer
B
0
Correct Answer
C
3
Your Answer
D
2

Solution

The correct option is D 3
Let ax2+bx+c=0    (1) has roots α,β
Equation having roots α2,β2 is f(x)=0
i.e., ax+bx+c=0
ax+c=bx
a2x2+(2acb2)x+c2=0     (2)

(1) and (2) represent the same equation.
a=a2, b=2acb2, c=c2
a=1 as a=0 is not possible
and c=0,1

Case 1: b=2acb2 and a=1,c=0
b+b2=0
b=0 or b=1
Possible quadratic equations are 
x2=0
x2x=0

Case 2: b=2acb2 and a=1,c=1
b2+b2=0
b=2 or b=1
Possible quadratic equations are 
x22x+1=0
x2+x+1=0, Not possible as it has non-real roots.

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