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Discriminant

The number of...

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

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B

0

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C

1

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D

2

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Solution

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

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