Write a polynomial function of least degree with integral coefficients that has the given zeros.

0, - 5, 3 + i

need to show all work

Question

Mathematics

Ronnie Dunlap

21 December, 18:19

Write a polynomial function of least degree with integral coefficients that has the given zeros.

0, - 5, 3 + i

need to show all work

+4

Answers (1)

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Rivers · Answer 1

The zeroes are

0, - 5, 3 + i (and its conjugate)

The factors are

x (x + 5) (x - (3 + i)) (x - (3 - i))

Expanding ...

(x² + 5x) ((x - 3) - i) ((x - 3) + i)

(x² + 5x) ((x - 3) ² - i²)

(x² + 5x) (x² - 6x + 9 - (-1))

(x² + 5x) (x² - 6x + 10)

x⁴ - 6x³ + 10x² + 5x³ - 30x² + 50x

x⁴ - x³ - 20x² + 50x

Write a polynomial function of least degree with integral coefficients that has the given zeros.0, - 5, 3 + ineed to show all work

Write a polynomial function of least degree with integral coefficients that has the given zeros.

0, - 5, 3 + i

need to show all work