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shtirl [24]
2 years ago
7

Using the given zero to find the remaining zeros of the function f(x)=x^3-4^2+49x-196; zero: -7i

Mathematics
1 answer:
natima [27]2 years ago
6 0
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.
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