If α<β are the roots of x²+bx+c=0 with c<0<b, then (a) 0<α<β (b) α<0<β<|α| (c) α<β<0 (d) α<0<|α|<β

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[JEE Advanced 2000] If $\alpha<\beta$ are the roots of $x^2+bx+c=0$ with $c<0<b$, then

VAVidaara Admin Asked 1mo ago 1 views 1 answer

If $\alpha<\beta$ are the roots of $x^2+bx+c=0$ with $c<0<b$, then

(a) $0<\alpha<\beta$
(b) $\alpha<0<\beta<|\alpha|$
(c) $\alpha<\beta<0$
(d) $\alpha<0<|\alpha|<\beta$

VAVidaara Admin ✓ Vidaara Team ✓ Accepted · 1mo ago ▲ 0

Correct answer: (b) $\alpha<0<\beta<|\alpha|$

Product $\alpha\beta=c<0$ gives opposite signs ($\alpha<0<\beta$); sum $\alpha+\beta=-b<0$ gives $|\alpha|>\beta$. So $\alpha<0<\beta<|\alpha|$.

JEE Advanced 2000 · Quadratic Equations and Inequations — verified solution by the Vidaara Team.

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