Integral roots
Find the total number of integral values of such that the equation has integral roots (of ).
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1 solution
Let two integral roots are p , q
Now p + q = − a and p q = a + 1
p + q + p q = − a + a + 1
p + q + p q = 1
1 + p + q + p q = 2
( p + 1 ) ( q + 1 ) = 2
As p and q are integers
Case(1): p + 1 = 2 and q + 1 = 1 or p + 1 = 1 and q + 1 = 2
From here a = − 1
Case(2) : p + 1 = − 2 and q + 1 = − 1 or p + 1 = − 1 and q + 1 = − 2
From here a = 5
So, a has two values a = − 1 , 5