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  4. The number of integral values of ' a ' for which the quadratic equation x2+(a+19) x+19 a+1=0 has integral roots, are

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Q. The number of integral values of ' $a$ ' for which the quadratic equation $x^2+(a+19) x+19 a+1=0$ has integral roots, are

Complex Numbers and Quadratic Equations

Solution:

$x^2+(a+19) x+19 a+1=0$
$(x+a)(x+19)=-1$
$( a \in I )$ and $( x \in I )$
Case(I) $x + a =1$ and
$ x+19=-1 $
$x=-20$
$a =21$
Case(II)
$x+a=-1 \text { and } x+19=1 $
$x =-18 $
$a =17$
Values of $a =17,21$
Number of values of $a=2$.