F(x) = 8891x
2 + ax + 1988, and:
G(x) = 1988x
2 + ax + 8891
Find the value of a such that F(x) and G(x) contain a common zero.
If a pair of polynomials have a common root then that root will also occur in any linear combination of the polynomials.
F(x)-G(x) = 6903x^2 - 6903 = 6903*(x-1)*(x+1)
So the possible common root is either x=1 or x=-1.
If x=1 then F(1)=G(1)=0=8891+a+1988, which makes a=-10879
If x=-1 then F(-1)=G(-1)=0=8891-a+1988, which makes a=10879
There are two values of a such that F(x) and G(x) contain a common zero: a=10879 and a=-10879.
Solution
