Cubic Polynomicals

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plac6636

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Aug 29, 2005
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The question is: "Find a cubic polynomial in standard form with real coefficients, having the roots of 0 and (4-3i)." So I know that if (4-3i) is a root then (4+3i) is also a root, and I need to multiply all three together to get the polynomial. I'm stuck though. I have (x-0)(x-4+3i)(x-4-3i), and I'm multplying the two with i. I have x^2-4x.....then is 3ix right? It doesn't seem right to me. What am I doing wrong?
 
plac6636 said:
(x-0)(x-4+3i)(x-4-3i)
Click to expand...
This is absolutely correct. What is NOT correct is your understanding of multiplying such things. You appear to be a victim of "FOIL". All you really need is an understanding of multiplication. Multiply EACH term in one factor by EACH term in the other factor. That's all it is.

(x-4+3i)(x-4-3i) = x*(x-4-3i) - 4*(x-4-3i) + 3i*(x-4-3i)

Down with "FOIL"!! Just learn multiplication.
 
#1) It's not my fault that teachers have taught me "FOIL" my whole life. Every time I come on here for help that is what I get and you make me feel stupid. I'm coming to you for help for a reason....that I don't know how to do it!
#2) Setting aside the fact that I don't know how to multiply...if I multiply x(x-4-3i) I still get x^2-4x-3ix....and so on. What do you do with 3ix?
 
Try to relax. Feeling stupid is optional. No one is making you feel that way. It is your choice. How about not chosing it? I think it's a great idea, not to choose to feel stupid.

You should not have to worry about the 'i's. If you picked the right factor, which you did, they will have companions that will cancel each other out. They all should go away.

Down with "FOIL". Your teacher should learn better, too.
 
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