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 #819295 by MathTherapy(10552)\"\" \"About 
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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.
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N = 3 indicates that there are 3 zeroes, or 3 solutions. One of the 3 zeroes or solutions is - 2, and the other 2 are:\r\n" );
document.write( "8 + 5i, and its CONJUGATE, 8 - 5i. \r\n" );
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document.write( "With the 3 zeroes/solutions being - 2, 8 + 5i, and 8 - 5i, it follows that, x = - 2, x = 8 + 5i, and x = 8 - 5i, thus \r\n" );
document.write( "making the function’s factors: x + 2, x - 8 - 5i, and x - 8 + 5i.\r\n" );
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document.write( "We now have the following function: f(x) = a(x + 2)(x - 8 - 5i)(x - 8 + 5i), which then becomes:\r\n" );
document.write( "     y = a(x + 2)[(x - 8)2 - (5i)2] ------ FOILing/Expanding (x - 8 - 5i)(x - 8 + 5i)\r\n" );
document.write( "    \"matrix%281%2C3%2C+y%2C+%22=%22%2C+a%28x+%2B+2%29%28%28x+-+8%29%5E2++-++25i%5E2%29%29\" \r\n" );
document.write( "    \"matrix%281%2C3%2C+y%2C+%22=%22%2C+a%28x+%2B+2%29%28%28x+-+8%29%5E2++-++25%28-+1%29%29%29\" \r\n" );
document.write( "  \"matrix%281%2C3%2C+244%2C+%22=%22%2C+a%282+%2B+2%29%28%282+-+8%29%5E2+%2B+25%29%29\" -------- Substituting f(2) = 244, or (2, 244) for (x, y) to determine value of “a”\r\n" );
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document.write( "With ”a” being 1, \r\n" );
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document.write( "This is your 3rd degree polynomial, or a polynomial with N = 3, and the given roots.
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