document.write( "Question 1188217: I haven't done this before. I'm so confused. N=3 -2 and 8+5i are zeros. F(2)=244. Says find the nth degree polynomial function with real coefficients satisfying the given conditions. \n" ); document.write( "

Algebra.Com's Answer #819255 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Apply these two rules:
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document.write( "1. Each zero b contributes a factor  (x-b)
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document.write( "2. Complex zeros (and roots) always come in conjugate pairs\r
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document.write( "The zero at 3  contributes  (x-3)
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document.write( "The zero at -2 contributes  (x-(-2)) = (x+2)
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document.write( "The zero at 8+5i and conjugate contribute  (x-8-5i)(x-8+5i)\r
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document.write( "Multiply all four of these factors, and simplify, to get:\r
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document.write( "But, this function has  g(2) = -244, and the problem states f(2)=244,
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document.write( "thus we need to multiply g(x) by -1, and the final answer is:\r
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document.write( "  \r
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document.write( "Note that f(x) is just g(x) flipped across the x-axis (mirror image).
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document.write( "----
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document.write( "EDIT 12/1 --  I see (now, after seeing MathTherapy's answer) that the intention was to indicate N=3 as the _DEGREE_ of the polynomial.  I interpreted N=3 as one of the zeros.   Thanks MathTherapy for catching that.  \r
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