How do you write a polynomial in standard form given the zeros x=1, -1, √3i, -√3i?

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How do you write a polynomial in standard form given the zeros x=1, -1, √3i, -√3i?

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Answer 1 · 2016-03-12T00:08:54

When we know the zeros of a polynomial $z_{i}$ $z_i$ , we can obtain the polynomial, by multiplying a constant different of zero, $a$ $a$ , by the product of all $(x - z_{i})$ $(x-z_i)$ .

If zeros are $1, - 1, \sqrt{3} i, - \sqrt{3} i$ $1, -1, sqrt(3)i, -sqrt(3)i$

The polynomial will be:

$a (x - 1) (x + 1) (x - \sqrt{3} i) (x + \sqrt{3} i)$ $a(x-1)(x+1)(x-sqrt(3)i)(x+sqrt(3)i)$

$a (x^{2} - 1) (x^{2} + 3)$ $a(x^2-1)(x^2+3)$

$a (x^{4} + 3 x^{2} - x^{2} - 3)$ $a(x^4+3x^2-x^2-3)$

$a (x^{4} + 2 x^{2} - 3)$ $a(x^4+2x^2-3)$ , where a is any real number except zero.

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How do you write a polynomial in standard form given the zeros x=1, -1, √3i, -√3i?

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