Question
Suppose a polynomial function of degree 4 with rational coefficients has the following given numbers as zeros. Find the other zero(s).
The other zero(s) is/are
(Type an exact answer, using radicals and
The other zero(s) is/are
(Type an exact answer, using radicals and
Ask by Vargas Dunn. in the United States
Mar 28,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The other zeros are
Solution
Since the polynomial has rational coefficients, the zeros must come in conjugate pairs.
- The given zero
implies that its complex conjugate is also a zero. - The given zero
implies that its conjugate is also a zero.
Thus, the other zeros are
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Simplify this solution Bonus Knowledge
Since the polynomial has rational coefficients, the complex zeros must come in conjugate pairs. Thus, the conjugate of the given zero
Also, the given zero
Therefore, the other zeros of the polynomial are
The other zero(s) is/are
