How do you write a polynomial function of least degree that has real coefficients, the following given zeros: $1, 1 + \sqrt{2}, 1 - \sqrt{2}$ $1, 1+sqrt(2), 1-sqrt(2)$ ?

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How do you write a polynomial function of least degree that has real coefficients, the following given zeros: $1, 1 + \sqrt{2}, 1 - \sqrt{2}$ $1, 1+sqrt(2), 1-sqrt(2)$ ?

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Answer 1 · 2016-07-25T08:31:03

$x^{3} - 3 x^{2} + x + 1$ $x^3 - 3 x^2 + x+1$

Explanation:

$(x - 1 - \sqrt{2}) (x - 1 + \sqrt{2}) (x - 1) = ({(x - 1)}^{2} - 2) (x - 1)$ $(x-1-sqrt(2))(x-1+sqrt(2))(x-1) = ((x-1)^2-2)(x-1)$
$= x^{3} - 3 x^{2} + x + 1$ $=x^3 - 3 x^2 + x+1$

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How do you write a polynomial function of least degree that has real coefficients, the following given zeros: $1, 1 + \sqrt{2}, 1 - \sqrt{2}$ $1, 1+sqrt(2), 1-sqrt(2)$ ?

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How do you write a polynomial function of least degree that has real coefficients, the following given zeros: 1,1+√2,1−√2 1, 1+sqrt(2), 1-sqrt(2)?

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Explanation:

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How do you write a polynomial function of least degree that has real coefficients, the following given zeros: $1, 1 + \sqrt{2}, 1 - \sqrt{2}$ $1, 1+sqrt(2), 1-sqrt(2)$ ?