Question

How do you write a polynomial in standard form given zeros 8, -14, and 3 + 9i?

Answer 1

`x^4-22x^2-10080=0`

Explanation:

Complex roots occur in conjugate pairs. So, the fourth root is `3-9i`.

If `s_1,s_2, s_3 and s_4` are the sums of the products of the roots, taken 1, 2, 3 and 4, at a time, respectively, the biquadratic equation has the form
`x^4-s_1x^3+s_2x^2-s_3x+s_4=0`.

Here, `s_1=0, s_2=-22, s_3=0 and s_4=-10080`.

So, the answer is `x^4-22x^2-10080=0`.

Note that the sum `3+-9i`=0,
wherever it occurs in the terms of s-sums.