find the number of integral values of a for which the quadratic equation (x + a)(x + 1991) + 1 - Maths - Complex Numbers and Quadratic Equations

Question

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

Neha Sethi · Accepted Answer

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

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