Chapter 4 - Polynomial and Rational Functions - 4.6 Complex Zeros; Fundamental Theorem of Algebra - 4.6 Assess Your Understanding - Page 240: 14

$2+i$ and $i$

Work Step by Step

The Conjugate Pairs Theorem says that if a polynomial has real coefficients, then any complex zeros occur in conjugate pairs. That is, if $a + bi$ is a zero then so is $a – bi$ and vice-versa. Its degree is $4$, hence it has $4$ complex (including real) zeros. $2$ zeros are already given, hence there are only $2$ zeros left which are $2+i$ and $i$ (the conjugates of $2-i$ and $-i$, respectively) according to the Conjugate Pairs Theorem.

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