document.write( "Question 1071605: Find a polynomial function of least degree having only real coefficients, a leading coefficient of 1, and zeros of 4 and 1+I. \n" ); document.write( "

Algebra.Com's Answer #686495 by Edwin McCravy(20056) $\"\"$ $\"About$

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Find a polynomial function of least degree having
\n" ); document.write( "only real coefficients, a leading coefficient of 1,
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document.write( "    x = 4           x = 1 + i           x = 1 - i\r\n" );
document.write( "x - 4 = 0   x - 1 - i = 0       x - 1 + i = 0\r\n" );
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document.write( "Multiply the three left sides together:\r\n" );
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document.write( "    (x - 4)(x - 1 - i)(x - 1 + i)\r\n" );
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document.write( "and set that product equal to the product of the\r\n" );
document.write( "three right sides (0)(0)(0)=0 \r\n" );
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document.write( "    (x - 4)(x - 1 - i)(x - 1 + i) = 0\r\n" );
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document.write( "(x - 4)[(x - 1) - i][(x - 1) + i] = 0\r\n" );
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document.write( "           (x - 4)[(x - 1)² - i²] = 0\r\n" );
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document.write( "         (x - 4)[(x - 1)² - (-1)] = 0\r\n" );
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document.write( "            (x - 4)[(x - 1)² + 1] = 0\r\n" );
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document.write( "         (x - 4)[x² - 2x + 1 + 1] = 0\r\n" );
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document.write( "             (x - 4)(x² - 2x + 2) = 0\r\n" );
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document.write( "     x³ - 2x² + 2x - 4x² + 8x - 8 = 0\r\n" );
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document.write( "               x³ - 6x² + 10x - 8 = 0\r\n" );
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document.write( "Edwin

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