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

1 Answer
Apr 23, 2016

Answer:

#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.