Answer:
x=0 and -2
Notice a n=8, g(n)=0 and f(x) = 0. If n<8, the coefficients for f(x) become negative and when n>8, the coefficients becomes positive. It won't affect x=0 because x can be factor out and be equal to zero but will affect the second zero
Step-by-step explanation:
Given: g(n) = 1/2*n - 4 and f(x)= g(n)x^2 + 2(g(n))x; n≠8
n = 2
g(n) = 1/2*n - 4
g(n) = 1/2*2 - 4 = 1-4 = -3
f(x)= g(n)x^2 + 2(g(n))x
f(x)= -3x^2 + 2(-3)x = -3x^2 - 6x
0= -3x^2 - 6x; factor out -3x
0 = -3x(x + 2)
-3x = 0; x=0
(x+2)= 0; x=-2
Notice a n=8, g(n)=0 and n<8, the coefficients for f(x) become negative and when n>8, the coefficients becomes positive
