Because \(f\) has real coefficients, you know the complex root occurs along with its conjugate. That is, both \(x=\pm7i\) are roots to \(f(x)\).
This means that dividing through by both factors yields another polynomial with no remainder:
\(\dfrac{x^3-4x^2+49x-196}{(x-7i)(x+7i)}=\dfrac{x^3-4x^2+49x-196}{x^2+49}=x-4\)
This means the last root (there are only three according to the fundamental theorem of algebra) is \(x=4\).
