Find a polynomial function of least degree having only real coefficients, a leading of 1, and zeros of 2 and 2+i.

Question

Find a polynomial function of least degree having only real coefficients, a leading of 1, and zeros of 2 and 2+i.

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Aubrey 2 weeks 2021-10-05T05:14:49+00:00 1 Answer 0

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    2021-10-05T05:16:34+00:00

    Answer:

    y = x³ − 6x² + 13x − 10

    Step-by-step explanation:

    Complex roots come in pairs, so if 2 + i is a root, then 2 − i is also a root.

    y = (x − 2) (x − (2 + i)) (x − (2 − i))

    y = (x − 2) (x − 2 − i) (x − 2 + i)

    y = (x − 2) ((x − 2)² − i²)

    y = (x − 2) (x² − 4x + 5)

    y = x (x² − 4x + 5) − 2 (x² − 4x + 5)

    y = x³ − 4x² + 5x − 2x² + 8x − 10

    y = x³ − 6x² + 13x − 10

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45:7+7-4:2-5:5*4+35:2 =? ( )