document.write( "Question 1056305: How to find the values of constants a and b if 2+3i is a
\n" ); document.write( "zero of the polynomial P(x) = ax^3 - 9x^2 + 30x - b? \n" ); document.write( "

Algebra.Com's Answer #671520 by Edwin McCravy(20056) $\"\"$ $\"About$

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How to find the values of constants a and b if 2+3i is a
\n" ); document.write( "zero of the polynomial P(x) = ax^3 - 9x^2 + 30x - b?
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document.write( "Since we are given that 2+3i is a zero, we know that if \r\n" );
document.write( "we substitute x = 2+3i in , we \r\n" );
document.write( "must get 0.  Substituting:\r\n" );
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document.write( "Since i²=-1\r\n" );
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document.write( "Then the real and the imaginary parts must both = 0\r\n" );
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document.write( "Setting the imaginary part = 0,\r\n" );
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document.write( "9a-18 = 0\r\n" );
document.write( "   9a = 18\r\n" );
document.write( "    a = 2\r\n" );
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document.write( "Setting the real part = 0\r\n" );
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document.write( "  -46a+105-b = 0\r\n" );
document.write( "-46(2)+105-b = 0\r\n" );
document.write( "   -92+105-b = 0\r\n" );
document.write( "        13-b = 0\r\n" );
document.write( "          13 = b\r\n" );
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document.write( "So\r\n" );
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document.write( "becomes\r\n" );
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document.write( "Edwin

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