Consider the equation {x^2} + alpha x + | vedclass

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Question

$\alpha, \beta$ are roots of $\mathrm{x}^{2}+\alpha \mathrm{x}+\beta=0$ is

$\alpha+\beta=-\alpha$         .......$(1)$

Vedclass · Accepted Answer

inequality is satisfied by exactly two integral values of $y$

Vedclass · Answer

$\alpha, \beta$ are roots of $\mathrm{x}^{2}+\alpha \mathrm{x}+\beta=0$ is

$\alpha+\beta=-\alpha$         .......$(1)$

and $\alpha \beta=\beta$           .......$(2)$

from $(1) $ and $(2) \alpha=1, \beta=-2$

Now $\| y+2|-1|<1$

$\Rightarrow-1<|\mathrm{y}+2|-1<1 \Rightarrow 0<|\mathrm{y}+2|<2$

$\Rightarrow-2<\mathrm{y}+2<2$ and $\mathrm{X} 
eq-2$

$\Rightarrow \mathrm{y} \in(-4,0)-\{-2\}$

Consider the equation ${x^2} + \alpha x + \beta = 0$ having roots $\alpha ,\beta $ such that $\alpha \ne \beta $ .Also consider the inequality $\left| {\left| {y - \beta } \right| - \alpha } \right| < \alpha $ ,then

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