Question 587785: I need to know how to write a polynomial equation of least degree with roots -3i, 3i, i, and -i. Can someone help me?
As a note, I am a high-school senior working on my precalculus book, but I am struggling with polynomials. This question comes from the first of five units for this course, and since math builds on itself, I find it necessary to ask for help before continuing on. I use a correspondance program for school and only have a textbook to teach me. There is no teacher I can contact, and no website or workbook to accompany it. My book has only shown me how to plug in roots to a provided equation for the purpose of checking whether or not they are actual roots. However, that is not enough for me to go on.
Can someone please explain to me, step-by-step, how I would solve this problem and others like it? I have not done so well during my last few math courses because it is hard to for me to comprehend a concept based on only one example provided by a textbook. Any help you can give will be greatly appreciated, and can you please show your work so I understand exactly the steps you used? Thanks again.
Answer by scott8148(6628)   (Show Source):
You can put this solution on YOUR website! if r is a root, then (x - r) is a factor
(x - -3i)(x - 3i)(x - -i)(x - i) = 0
(x + 3i)(x - 3i)(x + i)(x - i) = 0
FOILing (two pairs) ___ (x^2 - 9i^2)(x^2 - i^2) = 0
(x^2 + 9)(x^2 + 1) = 0
FOILing ___ x^4 + 10x^2 + 9 = 0
remember, i represents the square root of minus one; so i^2 equals -1
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