Please consider the following functions:
1. f(x) = x^2 - x + 1
2. g(x) = x + x^2 + x
Solve for c and d so that g(x) = 0 on the interval (c, d).
If a solution exists, enter the trivial solution {0, 0, 0}.
Determine whether f(a), f(b), f(c), and f(d) are linearly independent.
Need help.