Xenon B.

asked • 12/05/19# Write a polynomial function of least degree with integral coefficients that has the following zeros: -2, and 2-i

## 1 Expert Answer

Arturo O. answered • 12/05/19

Experienced Physics Teacher for Physics Tutoring

To ensure real coefficients, the complex conjugate of any complex zero must also be a zero. Therefore you must have at least 3 zeros:

-2

2 - i

2 + i

f(x) = A(x + 2) [x - (2 - i)] [x - (2 + i)]

with A real, integer, and A ≠ 0. You can expand f(x) to standard form if you wish. The coefficients will come out real.

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Arturo O.

Do you also require real coefficients?12/05/19