jmc

Question

Find all values of b for which the equations 1988x^2 + bx + 8891 = 0 and 8891x^2 + bx + 1988 = 0 have a common root. Enter all the possible values of b, separated by commas.

Accepted Answer

Let r be a common root, so align* 1988r^2 + br + 8891 &= 0, 8891r^2 + br + 1988 &= 0. align*Subtracting these equations, we get 6903r^2 - 6903 = 6903 (r^2 - 1) = 0, so r = 1. If r = 1, then 1988 + b + 8891 = 0, so b = -10879. If r = -1, then 1988 - b + 8891 = 0, so b = 10879.