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  4. The sum of integral values of α for which the equation (x + α )(x + 1991)+1=0 has integral roots is/are

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Q. The sum of integral values of $\alpha $ for which the equation $\left(x + \alpha \right)\left(x + 1991\right)+1=0$ has integral roots is/are

NTA AbhyasNTA Abhyas 2022

Solution:

$\left(x + \alpha \right)=1$ and $x+1999=-1\Rightarrow \alpha =1993$
$x+\alpha =-1$ and $x+1991=1,\alpha =1989$
Sum $=1993+1989$