Question

The number of integral values of a for which the quadratic equation $(x+a)(x+1991)+1=0$ has integral roots are

• A. $3$
• B. $1$
• C. $0$
• D. $2$

Answer 1

The correct option is D

$2$

$(x+a)(x+1991)+1=0$

$\Rightarrow (x+a)(x+1991)=-1$

$\Rightarrow (x+a)=1$ and $x+1991=-1$

$\Rightarrow a=1993$ or $x+a=-1$ and $x+1991=1$

$\Rightarrow a=1993$ or $a=1989$