document.write( "Question 360526: How many imaginary zeros does the function f(x) = 3x4 + 2x3 + 4x + 7 have? \n" ); document.write( "

Algebra.Com's Answer #257223 by Edwin McCravy(20059) $\"\"$ $\"About$

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document.write( "By DesCarte's rule of signs:\r\n" );
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document.write( "There are no sign changes going left to right, \r\n" );
document.write( "so it has 0 positive zeros\r\n" );
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document.write( "Now we find f(-x)\r\n" );
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document.write( "There are 2 sign changes going left to right, \r\n" );
document.write( "so f(x) has either 2 negative zeros or 0 negative zeros.\r\n" );
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document.write( "A fourth degree equation has 4 zeros counting multiplicity,\r\n" );
document.write( "and its imaginary zeros come in conjugate pairs. \r\n" );
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document.write( "So the equation either has 2 negative zeros and one pair of\r\n" );
document.write( "conjugate imaginary zeros or else it has 0 negative zeros\r\n" );
document.write( "and two pairs of conjugate imaginary zeros, i.e., 4 imaginary\r\n" );
document.write( "zeros.\r\n" );
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document.write( "Edwin

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