How do you write a polynomial function of least degree and leading coefficient 1 when the zeros are 8, -i, i?

1 Answer
A. S. Adikesavan
Jul 14, 2016

x^3-8x^2+x-6x3−8x2+x−6

Explanation:

The polynomial with zeros x_1, x_2 and x_3x1,x2andx3 is

x^3-(x_1+x_2+x_3)x^2+(x_2x_3+x_3x_1+x_1x_2)x-x_1x_2x_3x3−(x1+x2+x3)x2+(x2x3+x3x1+x1x2)x−x1x2x3

Here, it is

x^3-(8+i-i)x^2+(-i^2-8i+8i)x-(9)(i)(-i)x3−(8+i−i)x2+(−i2−8i+8i)x−(9)(i)(−i)

=x^3-8x^2+x-6=x3−8x2+x−6

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