Question 141
It is given that the real roots of the quadratic polynomial $g(x) = x^2 - 3x + a$ are also roots of the polynomial $f(x) = x^3 - x^2 + c x + 4$. Analogously, both real roots of the quadratic polynomial $h(x) = x^2 + x + b$ are also roots of $f(x)$. What values can $f(1)$ take?