document.write( "Question 880837: Find an nth degree polynomial function with real coefficients satisfying the given conditions. N=3; -5 and 4 + 3i are zeros; f(2) = 91
\n" ); document.write( "My math book doesnt give an example for this problem so im confused, i just know a=-1
\n" ); document.write( "And the problem should end up as x^3-3x^2-15x+125 \n" ); document.write( "

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Find an nth degree polynomial function with real coefficients satisfying the given conditions. N=3; -5 and 4 + 3i are zeros; f(2) = 91
\n" ); document.write( "My math book doesnt give an example for this problem so im confused, i just know a=-1
\n" ); document.write( "And the problem should end up as x^3-3x^2-15x+125
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document.write( "n = 3 indicates that there are 3 zeroes, or 3 solutions to the equation. Two of the 3 zeroes or solutions
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document.write( "are - 5 and 4 + 3i, but complex numbers such as 4 + 3i come in CONJUGATE PAIRS. The conjugate of 4 + 3i is: 4 – 3i\r
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document.write( "Now, we have 3 zeroes/solutions, as follows: x = - 5; x = 4 + 3i, and x = 4 - 3i
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document.write( "x =  - 5________x + 5      = 0
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document.write( "x =    4 + 3i___x – 4 - 3i = 0
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document.write( "x =    4 - 3i___x - 4 + 3i = 0\r
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document.write( "We now have the following:
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document.write( "f(x) = a(x + 5)(x – 4 - 3i)(x - 4 + 3i)
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document.write( " ------ Expanding (x – 4 - 3i)(x - 4 + 3i)
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document.write( " -------- Substituting 2 for x to determine value of a
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document.write( "f(2) = a(7)(4 - 16 + 25)
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document.write( "f(2) = 7a(13)
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document.write( "f(2) = 91a\r
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document.write( "Now, since f(2) = 91, then we can say that: 91 = 91a -----  ----- 1 = a
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document.write( "Therefore, f(x) = a(x + 5)(x – 4 - 3i)(x - 4 + 3i) becomes , or 
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document.write( "Expand these polynomials to obtain the 3rd degree polynomial. \n" );
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