[JEE Advanced 2000] If $\alpha,\beta$ are roots of $ax^2+bx+c=0$ and $\alpha+\delta,\beta+\delta$ of $Ax^2+Bx+C=0$, prove $\dfrac{b^2-4ac}{a^2}=\dfrac{B^2-4AC}{A^2}$.
If $\alpha,\beta$ are roots of $ax^2+bx+c=0$ and $\alpha+\delta,\beta+\delta$ of $Ax^2+Bx+C=0$, prove $\dfrac{b^2-4ac}{a^2}=\dfrac{B^2-4AC}{A^2}$.
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VAVidaara Admin
✓ Vidaara Team
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· 1mo ago
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Answer: Proved.
Both sides equal $(\alpha-\beta)^2$, since a shift by $\delta$ leaves the difference of roots unchanged: $(\alpha+\delta)-(\beta+\delta)=\alpha-\beta$.
JEE Advanced 2000 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.
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