document.write( "Question 919829: Write a polynomial function of least degree that has the given zeros \r
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Algebra.Com's Answer #557985 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Write a polynomial function of least degree that has the given zeros \r
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document.write( "Since 3+2i is a solution, then 3-2i must also be a solution if the resulting\r\n" );
document.write( "polynomial is to have all real coefficients.\r\n" );
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document.write( "Start with these three equations for \"x = ↏\"\r\n" );
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document.write( "x = -5,  x = 3+2i, and we must also include x = 3-2i\r\n" );
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document.write( "Get 0 on the right of each\r\n" );
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document.write( "x+5 = 0, x-3-2i = 0, x-3+2i = 0\r\n" );
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document.write( "Multiply equals by equals:\r\n" );
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document.write( "(x+5)(x-3-2i)(x-3+2i) = 0\r\n" );
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document.write( "Group the (x-3)'s\r\n" );
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document.write( "(x+5)[(x-3)-2i][(x-3)+2i] = 0\r\n" );
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document.write( "Multiply the last two factors:\r\n" );
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document.write( "(x+5)[(x-3)²-4i²] = 0\r\n" );
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document.write( "(x+5)[(x-3)²-4(-1)] = 0\r\n" );
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document.write( "(x+5)[(x-3)²+4] = 0\r\n" );
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document.write( "(x+5)[(x-3)(x-3)+4] = 0\r\n" );
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document.write( "(x+5)[x²-6x+9+4] = 0\r\n" );
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document.write( "(x+5)[x²-6x+13] = 0\r\n" );
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document.write( "x³-6x²+13x+5x²-30x+65\r\n" );
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document.write( "x³-x²-17x+65 = 0\r\n" );
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document.write( "So the function of least degree with real coefficients \r\n" );
document.write( "that has those zeros is\r\n" );
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document.write( "f(x) = x³-x²-17x+65\r\n" );
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document.write( "[Note:  If the problem did not state \"with real coefficients\", then \r\n" );
document.write( "this: f(x) = x²+(2-2i)x-(10i+15), with imaginary coefficients would  \r\n" );
document.write( "be the polynomial with least degree, but I'm almost sure the problem \r\n" );
document.write( "stated \"with real coefficients\".] \r\n" );
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\n" ); document.write( "...and also -1, 5, 2
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document.write( "Start with these three equations for \"x = ↏\"\r\n" );
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document.write( "x = -1, x = 5, x = 2\r\n" );
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document.write( "Do the same as above and see if you can get\r\n" );
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document.write( "f(x) = x³-6x²+3x+10\r\n" );
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document.write( "Edwin
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