341He means that if α,β are roots of ax2+bx+c=0 then α2,β2 are also roots of the same equation.
Number of quadratic equations with real roots which remain unchanged even after sqaring their roots is
1. 1
2. 2
3. 3
4. 5
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7 Answers
341
62let the roots be p, q
then p2, q2 are also the roots..
ie p=p2, q=q2
The possibilities it leaves are 1, 1 or 1, 0 or 0, 0
Now also if we have p=q2 and q=p2 leaves us with the possibilities that p=w or w2
Thus, there should be 4 such equations...
namely
x2, x2-x, (x-1)2, 1+x+x2
341thats the complete list. but since only real solutions are allowed, you get 3 quadratics that fit the bill.
