SOLUTION: This is an update of a previous problem which I copied wrong
I need to find a polynomial of degree 4 with integer coefficients that have roots:-2,5,and 3+2i such that P(3)=-80. I
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Question 190966: This is an update of a previous problem which I copied wrong
I need to find a polynomial of degree 4 with integer coefficients that have roots:-2,5,and 3+2i such that P(3)=-80. I know to use the conjugate of 3+2i which is 3-2i, and I know how to put them in the f(x)=a(x-r1)(x-r2...format, but from there I get tripped up and can't figure out what to do with P(3)=-80. Thanks.
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
So far, so good. You have:
 = (x + 2)(x - 5)\left(x - (3 + 2i)\right)\left(x - (3 - 2i)\right))
Now you have to multiply those 4 binomials together. Use FOIL for the two pairs of binomials and the extension of the FOIL idea to multiply the two trinomials that will result. Hint: Treat the complex numbers as a single number when you multiply the two complex factors. Once you have your polynomial function in standard form, i.e.
 = \alpha_0x^4 + \alpha_1x^3 + \alpha_2x^2 + \alpha_3x + \alpha_4)
,
then
 = \alpha_0(3)^4 + \alpha_1(3)^3 + \alpha_2(3)^2 + \alpha_3(3) + \alpha_4)
John
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