JEE Advance - Mathematics (2001 - No. 16)
Let $$a,\,b,\,c$$ be real numbers with $$a \ne 0$$ and let $$\alpha ,\,\beta $$ be the roots of the equation $$a{x^2} + bx + c = 0$$. Express the roots of $${a^3}{x^2} + abcx + {c^3} = 0$$ in terms of $$\alpha ,\,\beta \,$$.
$$\alpha^2\beta, \alpha\beta^2$$
$$\alpha^3, \beta^3$$
$$\frac{\alpha}{\beta}, \frac{\beta}{\alpha}$$
$$\alpha+\beta, \alpha-\beta$$
$$\frac{\alpha^2}{\beta}, \frac{\beta^2}{\alpha}$$
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