Question 190967: 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 stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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P(x) = a(x+2)(x-5)(x-(3+2i))(x-(3-2i))
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Use P(3) = -80 to determine the value of "a":
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P(3) = a(5)(-2)(-2i)(2i) = -80
a(-10)(4) = -80
a(-40) = -40
a = 2
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Now you know the equation is:P(x) = 2(x+2)(x-5)(x-(3+2i))(x-(3-2i))
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Cheers,
Stan H.
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