find the number of integral values of a for which the quadratic equation (x + a)(x + 1991) + 1 = 0 has integral roots Share with your friends Share 0 Neha Sethi answered this Dear student We havex+ax+1991+1=0⇒x+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=-1⇒x=-1992Putting in 1 the value of x, we get-1992+a=1⇒a=1993Case2: x+a=-1 ...2 and x+1991=1 Since ab=-1⇒ we can take a=-1 and b=1Consider x+1991=1⇒x=-1990Putting in 2 the value of x, we get-1990+a=-1⇒a=1989So, number of integral values of a is 2 Regards 7 View Full Answer