If α,β are roots of ax²+bx+c=0 and α+δ,β+δ of Ax²+Bx+C=0, prove b²-4ac a² = B²-4AC A².

Answer: Proved. Both sides equal (α-β)², since a shift by δ leaves the difference of roots unchanged: (α+δ)-(β+δ)=α-β. JEE Advanced 2000 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

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[JEE Advanced 2000] if alpha beta are roots of ax 2 bx c 0 and alpha delta

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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 ✓ Accepted · 2d ago ▲ 0

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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