document.write( "Question 949929: Apply Descartes' Rule of Signs to f(x)=5x^3 - x^2 - 1 to determine the number of positive and negative zeros.
\n" ); document.write( "a) # of positive zeros:
\n" ); document.write( "b) # of negative zeros: \n" ); document.write( "

Algebra.Com's Answer #580007 by Theo(13342) $\"\"$ $\"About$

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here's a tutorial on descarted rule of signs.
\n" ); document.write( "http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut38_zero1.htm
\n" ); document.write( "f(x) = 5x^3 - x^2 - 1
\n" ); document.write( "signs are + - -
\n" ); document.write( "there is one sign change so there will be one positive real root.
\n" ); document.write( "f(-x) = 5(-x)^3 - (-x)^2 - 1
\n" ); document.write( "this simplifies to:
\n" ); document.write( "f(-x) = -5x^3 - x^2 - 1
\n" ); document.write( "signs are - - -
\n" ); document.write( "there are no sign changes.
\n" ); document.write( "there are no negative real roots.
\n" ); document.write( "since the degree of the equation is 3 and there is only 1 positive real root, then the number of complex roots must be equal to 2.
\n" ); document.write( "the graph of your equation is shown below:
\n" ); document.write( " $\"graph%28600%2C600%2C-10%2C10%2C-10%2C10%2C5x%5E3-x%5E2-1%29\"$
\n" ); document.write( "there is one positive root.
\n" ); document.write( "since the degree of the equation is 3, there must be 3 roots.
\n" ); document.write( "2 of them must be complex.
\n" ); document.write( "1 of them is positive.
\n" ); document.write( "none of them are negative.
\n" ); document.write( "real roots cross the x-axis.
\n" ); document.write( "complex roots don't.\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "

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