If α and β(α<β)  are the roots of the equation x2+bx+c=0,where c<0

If   are the roots of the equation

1. A

$0<\mathrm{\alpha }<\mathrm{\beta }$

2. B

$\mathrm{\alpha }<0<\mathrm{\beta }<|\mathrm{\alpha }|$

3. C

$\mathrm{\alpha }<\mathrm{\beta }<0$

4. D

$\mathrm{\alpha }<0<|\mathrm{\alpha }|<\mathrm{\beta }\mid$

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Solution:

Since are the roots of the equation ${\mathrm{x}}^{2}+\mathrm{bx}+\mathrm{c}=0.$Here,so, roots are real and unequal.
Now ,
$\therefore$ One root is positive and the other is negative, then the negative root being numerically bigger. As, is the negative root while $\beta$is the positive root. so$|\mathrm{\alpha }|>\mathrm{\beta }$
and  $\mathrm{\alpha }<0<\mathrm{\beta }$

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