Q13/058) For what values of b do the equation 1988x^2+bx+8891=0 and 8891x^2+bx+1988=0 have a common root?

we are given

 1988x^2+bx+8891=0 .. (1)

8891x^2+bx+1988=0.. (2)

We can eliminate x^2 from both to get

8891(1988x2+bx+8891) – 1988(8891x2+bx+1988) = 0

Or bx(8891-1988) = 1988^2- 9981 => bx = - (8891 + 1988)  = - 10879 ..3

Subtracting  2^nd one from 1^st we get (1988-8891) x^2 + (8891 – 1988) = 0 or x^2 = 1 +> x = 1 or – 1

From (3) if x = 1 then b = - 10879 and if x = - 1 then b = 10879