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

Question

The number of integral values of ' a ' for which the quadratic equation x2+(a+19) x+19 a+1=0 has integral roots, are (A) 0 (B) 1 (C) 2 (D) 3

Tardigrade Admin · Accepted Answer

x2+(a+19) x+19 a+1=0 (x+a)(x+19)=-1 ( a ∈ I ) and ( x ∈ 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.

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

0

1

2

3

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

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

0

1

2

3

x2+(a+19)x+19a+1=0 (x+a)(x+19)=−1 (a∈I) and (x∈I) Case(I) x+a=1 and x+19=−1 x=−20 a=21 Case(II) x+a=−1 and x+19=1 x=−18 a=17 Values of a=17,21 Number of values of a=2.

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

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