IIT-JEE 2000 ScreeningQuestion 1
If $\alpha$ and $\beta$ $(\alpha<\beta)$ are the roots of the equation $x^{2}+bx+c=0$, where $c<0<b$, then
Quadratic Equation · Location of Roots
Solution
Concept. The product decides whether the signs differ; the sum decides which root is larger in size. Formulas used. (1) $\alpha\beta=c$, $\alpha+\beta=-b$Step 1 - Product. $\alpha\beta=c<0$, so the roots have opposite signs: $\alpha<0<\beta$. Step 2 - Sum. $\alpha+\beta=-b<0$, so $\beta<-\alpha=|\alpha|$. Step 3 - Conclude. $\alpha<0<\beta<|\alpha|$. Answer: (B)