poloynomial function

Write a polynomial function f of least degree that has rational coefficients, a leading coefficient of 1, and the given zeros.



1) -2, -1, 1

2) i, 4

3) i, 2 - √3

4) 1, 4, 1 + √2

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  1. 2) x^3 - 4x^2 + x - 4
    extra credit: why a cubic, not a quadratic?

    4) x^3 - (6+√2)x^2 + (9+5√2)x - 4(1+√2)
    minimum degree. To get rid of the √2, add a root of 1-√2 to get
    x^4 - 7x^3 + 13x^2 - 3x - 4

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  2. -12-18i

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