(B) Given the quadratic equation $x^2 + bx + c = 0$ with $c 0$ and $c < 0$,$-4c

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$\alpha < 0 < \beta < |\alpha|$

(B) Given the quadratic equation $x^2 + bx + c = 0$ with $c First,calculate the discriminant $D = b^2 - 4c$. Since $b^2 > 0$ and $c 0$,so $D = b^2 - 4c > 0$. Thus,the roots are real and distinct.From the relation between roots and coefficients:Sum of roots: $\alpha + \beta = -b$. Since $b > 0$,$\alpha + \beta Product of roots: $\alpha \beta = c$. Since $c Since the product $\alpha \beta Since the sum $\alpha + \beta Given $\alpha Therefore,$|\alpha| > \beta$,which implies $\alpha < 0 < \beta < |\alpha|$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Relation between roots and coefficients

Medium

If $\alpha$ and $\beta$ $(\alpha < \beta)$ are the roots of the equation $x^2 + bx + c = 0,$ where $c < 0 < b,$ then

IIT 2000 All IIT

A
$0 < \alpha < \beta$
B
$\alpha < 0 < \beta < |\alpha|$
C
$\alpha < \beta < 0$
D
$\alpha < 0 < |\alpha| < \beta$

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4-2.Quadratic Equations and Inequations

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Relation between roots and coefficients

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