document.write( "Question 960679: Conjugate Zeros Theorem\r
\n" ); document.write( "\n" ); document.write( "Verify that the indicated complex number is a zero of the given polynomial function f.
\n" ); document.write( "1 + i; f(x) = 12x^4 − 23x^3 + 21x^2 + 4x − 2
\n" ); document.write( "Use the conjugate zeros theorem and long division to find all other zeros.\r
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Algebra.Com's Answer #587198 by MathLover1(20850)\"\" \"About 
You can put this solution on YOUR website!
Conjugate Zeros Theorem states: \r
\n" ); document.write( "\n" ); document.write( "if \"1+%2B+i\" is zero, then \"1+-+i\" is zero too\r
\n" ); document.write( "\n" ); document.write( "so, the product \"%281+%2B+i%29%281+-+i%29=1%5E2-i%5E2=1-%28-1%29=1%2B1=2\" is a factor of\r
\n" ); document.write( "\n" ); document.write( "\"f%28x%29+=+12x%5E4+-23x%5E3+%2B+21x%5E2+%2B+4x+-2\" ......so,divide by \"2\"\r
\n" ); document.write( "\n" ); document.write( "\"f%28x%29+=+%2812x%5E4-23x%5E3+%2B+21x%5E2+%2B+4x+-2%29%2F2\"\r
\n" ); document.write( "\n" ); document.write( "\"f%28x%29+=++%281%2F2%29%2812x%5E4+-23x%5E3+%2B+21x%5E2+%2B+4x+-2%29\".......factor \"%2812x%5E4+-23x%5E3+%2B+21x%5E2+%2B+4x+-2%29\"\r
\n" ); document.write( "\n" ); document.write( "\"f%28x%29+=+%281%2F2%29%2812x%5E4+-24x%5E3+%2Bx%5E3%2B+24x%5E2+-2x%5E2%2B+2x+-x%5E2%2B2x-2%29\"......group\r
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\n" ); document.write( "\n" ); document.write( "\"f%28x%29+=%281%2F2%29+%2812x%5E2%2B4x-3x-1%29+%28x%5E2-2x%2B2%29\"\r
\n" ); document.write( "\n" ); document.write( "\"f%28x%29+=%281%2F2%29+%28%2812x%5E2%2B4x%29-%283x%2B1%29%29+%28x%5E2-2x%2B2%29\"\r
\n" ); document.write( "\n" ); document.write( "\"f%28x%29+=%281%2F2%29+%284x%283x%2B1%29-%283x%2B1%29%29+%28x%5E2-2x%2B2%29\"\r
\n" ); document.write( "\n" ); document.write( "\"f%28x%29+=%281%2F2%29+%284x-1%29+%283x%2B1%29+%28x%5E2-2x%2B2%29\"\r
\n" ); document.write( "\n" ); document.write( "zeros:\r
\n" ); document.write( "\n" ); document.write( "\"%284x-1%29+=0\" =>\"highlight%28x=1%2F4%29+\"\r
\n" ); document.write( "\n" ); document.write( "\"%283x%2B1%29=0\" =>\"highlight%28x=-1%2F3%29\"\r
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\n" ); document.write( "\n" ); document.write( "\"x%5E2-2x%2B2=0+\"=>use quadratic formula\r
\n" ); document.write( "\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\" \r
\n" ); document.write( "\n" ); document.write( "\"x+=+%28-%28-2%29+%2B-+sqrt%28+%28-2%29%5E2-4%2A1%2A2+%29%29%2F%282%2A1%29+\"\r
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\n" ); document.write( "\n" ); document.write( "\"x+=+%282+%2B-+sqrt%28+4-8+%29%29%2F2+\" \r
\n" ); document.write( "\n" ); document.write( "\"x+=+%282+%2B-+sqrt%28+-4+%29%29%2F2+\" \r
\n" ); document.write( "\n" ); document.write( "\"x+=+%282+%2B-+2i%29%2F2+\" \r
\n" ); document.write( "\n" ); document.write( "\"x+=+%281+%2B-+i%29+\"\r
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\n" ); document.write( "\n" ); document.write( " =>\"highlight%28x+=+1%2Bi%29\" and \"highlight%28x+=+1-i%29\"\r
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