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