Multiple choice

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

  1. $3$
  2. $0$
  3. $1$
  4. $2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

(x+a)(x+1991) = -1. Let x+a = u and x+1991 = v. Then uv = -1. Since x is an integer, u and v are integers. The factors of -1 are (1, -1) and (-1, 1). Case 1: x+a = 1 and x+1991 = -1 => x = -1992, a = 1993. Case 2: x+a = -1 and x+1991 = 1 => x = -1990, a = 1989. Two values for a.

Keep practicing — related questions