If α,β are roots of ax²+bx+c=0, express the roots of a³x²+abcx+c³=0 in terms of α,β.

Answer: α²β and αβ². The new equation has sum of roots -(abc)/(a³)=(α+β)(αβ) and product (c³)/(a³)=(αβ)³, matching α²β and αβ². JEE Advanced 2001 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

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[JEE Advanced 2001] if alpha beta are roots of ax 2 bx c 0 express the roots

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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 ✓ Accepted · 2d ago ▲ 0

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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