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andrey2020 [161]
4 years ago
7

Using the given zero, find one other zero of f(x). 2 - 4i is a zero of f(x).= x4 - 4x3 + 21x2 - 4x + 20

Mathematics
1 answer:
OLEGan [10]4 years ago
5 0
<h3>Answer:</h3>

2 + 4i

<h3>Explanation:</h3>

Complex roots of polynomials with real coefficients come in conjugate pairs. The conjugate of a complex number has the same real part, but an imaginary part with opposite sign. (It is sometimes indicated using an asterisk.)

(2 - 4i)* = 2 + 4i . . . . . . the other complex root of this conjugate pair

_____

Factoring out (x² -4x +20) from f(x) gives (x² +1). Its roots are ±i, so are not on the list of answer choices.

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