How do you write a polynomial function of least degree with integral coefficients that has the given zeros 3, 1, -2, -4?

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How do you write a polynomial function of least degree with integral coefficients that has the given zeros 3, 1, -2, -4?

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Answer 1 · 2016-10-01T11:09:13

$x^{4} + 2 x^{3} - 13 x^{2} - 14 x + 24$ $color(green)(x^4+2x^3-13x^2-14x+24)$

Explanation:

If the polynomial has zeros at
$XXX 3, 1, - 2, - 4$ $color(white)("XXX")color(red)(3), color(blue)(1), color(magenta)(-2),color(orange)(-4)$
then it has factors
$XXX (x - 3), (x - 1), (x - (- 2)), (x - (- 4))$ $color(white)("XXX")(x-color(red)(3)), (x-color(blue)1), (x-color(magneta)(""(-2))), (x-color(orange)(""(-4)))$

$(x - 3) \cdot (x - 1) \cdot (x + 2) \cdot (x + 4)$ $(x-3) * (x-1) * (x+2) * (x+4)$

$XXXXXXXXX = x^{4} + 2 x^{3} - 13 x^{2} - 14 x + 24$ $color(white)("XXXXXXXXX")=x^4+2x^3-13x^2-14x+24$

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How do you write a polynomial function of least degree with integral coefficients that has the given zeros 3, 1, -2, -4?

1 Answer

Explanation:

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