JEE Advance - Mathematics (1989 - No. 12)
If $$\alpha $$ and $$\beta $$ are the roots of $${x^2}$$+ px + q = 0 and $${\alpha ^4},{\beta ^4}$$ are the roots of $$\,{x^2} - rx + s = 0$$, then the equation $${x^2} - 4qx + 2{q^2} - r = 0$$ has always
two real roots
two positive roots
two negative roots
one positive and one negative root.