document.write( "Question 433594: what does descrates rule of signs tell me about number of real positive zeros and negative real zeros of this function. 5x raised to the 6th-3x raised to the 3rd+x squared-x? \n" ); document.write( "

Algebra.Com's Answer #300579 by robertb(5830) $\"\"$ $\"About$

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Descartes' rule of signs only gives insight on whether a root is positive or negative, not whether a root is zero.
\n" ); document.write( "The polynomial $\"5x%5E6+-+3x%5E3+%2B+x%5E2+-+x+=+x%285x%5E5+-+3x%5E2+%2B+x%5E1+-+1%29\"$ has a root of 0. Thus apply Descartes' rule only on $\"5x%5E5+-+3x%5E2+%2B+x%5E1+-+1\"$ . Hence, there might 3 positive roots or 1 positive root. (3 variation of signs.)
\n" ); document.write( "Considering $\"-5x%5E5+-+3x%5E2+-+x%5E1+-+1\"$ , (replacing x by -x), we see that there are no negative roots. (No variation of signs.)
\n" ); document.write( "Hence the original polynomial have 0 as a root, 3 positive roots, and 2 complex roots, \r
\n" ); document.write( "\n" ); document.write( "OR\r
\n" ); document.write( "\n" ); document.write( "have 0 as a root, 1 positive root, and 4 complex roots. \n" ); document.write( "

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