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I have a question that is: Find a degree 3 polynomial with real coefficients whose leading coefficient is 5 that has -2, 1, and 4 as zeros?

I do not want the question answered for me what I want it explained what it is asking. I answered 5(x+2)(x-1)(x-4), but I was told I needed to finish the problem. Not exactly sure what there is to finish.

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They probably want you to distribute... sigh. – Mariano Suárez-Alvarez Jan 6 '11 at 2:07
up vote 6 down vote accepted

I think it is asking for a polynomial in the form $5x^3 + ax^2 + bx + c$.

So you would multiply out your answer.

As an aside, if that is what it is, it is a silly question. Your answer is fine, IMO.

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yeah, well every teacher has their quirks and you kinda don't have a choice but to go along – chromedude Jan 6 '11 at 2:12
@chrome: Or you can point them to this thread :-) – Aryabhata Jan 6 '11 at 2:20
yeah, big chance of that going over well ;) – chromedude Jan 6 '11 at 2:26
@chrome: Yeah... :-) – Aryabhata Jan 6 '11 at 2:27

After pointing out that this is the polynomial you are suggesting you need to show that it is indeed of the intended degree and have the wanted roots, and that the coefficients are real.

Simplify the given polynomial, it should be enough.

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