[JEE Advanced 2001] If $\alpha,\beta$ are roots of $ax^2+bx+c=0$, express the roots of $a^3x^2+abcx+c^3=0$ in terms of $\alpha,\beta$.
If $\alpha,\beta$ are roots of $ax^2+bx+c=0$, express the roots of $a^3x^2+abcx+c^3=0$ in terms of $\alpha,\beta$.
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VAVidaara Admin
✓ Vidaara Team
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· 1mo ago
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Answer: $\alpha^2\beta$ and $\alpha\beta^2$.
The new equation has sum of roots $-\frac{abc}{a^3}=(\alpha+\beta)(\alpha\beta)$ and product $\frac{c^3}{a^3}=(\alpha\beta)^3$, matching $\alpha^2\beta$ and $\alpha\beta^2$.
JEE Advanced 2001 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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