# Math

Suppose \$p(x)\$ is a monic cubic polynomial with real coefficients such that \$p(3-2i)=0\$ and \$p(0)=-52\$.

Determine \$p(x)\$ (in expanded form).

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3. 👁 456
1. john is 30 pounds heavier than peter. their total weight 235 pounds.find johns weight

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posted by sam
2. peter is 30 lbs lighter than john. So,

j + j-30 = 235

Odd; I expected an integer answer...

as for the polynomial, who knows? I see no question there. And LaTex doesn't do well here. And p(x) cannot be monic with real coefficients and have a complex root.

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posted by Steve
3. ah, actually I misspoke.

Since 3+2i is also a root, we have

p(x) = (x-(3-2i))(x-(3+2i))(x-a)
= (x^2-6x+13)(x-a)

So, now just solve for a:

p(0) = -13a = -52
a = 4

p(x) = (x^2-6x+13)(x-4) = x^3-10x^2+37x-52

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posted by Steve
4. Thanks so much :)

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posted by Eka

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