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

Dear student

We havex+ax+1991+1=0x+ax+1991=-1Case I:x+a=1  ...1 and x+1991=-1  Since ab=-1 we can  take a=1 and b=-1Consider,  x+1991=-1x=-1992Putting in 1 the value of x, we get-1992+a=1a=1993Case2:   x+a=-1  ...2 and x+1991=1 Since ab=-1 we can  take a=-1 and b=1Consider x+1991=1x=-1990Putting in 2 the value of x, we get-1990+a=-1a=1989So, number of integral values of a  is 2
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