Question

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

a.1 + i
b.1
c.1 - i
d.2 + 4i

Answer 1

2 + 4i

Step-by-step explanation:

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

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