Multiple choice

If $\displaystyle \alpha ,\beta $ are the roots of the equation $\displaystyle x^{2}+\alpha x+\beta =0$ such that $\displaystyle\alpha \neq \beta $ and $\displaystyle ||x-\beta |-\alpha| < 1 ,$ then

  1. inequality is satisfied by exactly three integral values of $x$
  2. inequality is satisfied by all values of $\displaystyle x \, \varepsilon \, (-4,-2)$
  3. roots of the equation are opposite in sign

  4. All of the above

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D Correct answer