document.write( "Question 1134149: Indentify the number of positive, negative, and imaginary roots, all rational roots , and the total amount of roots.
\n" ); document.write( "4x^4-3x^3+2x^2-x+1=0 \n" ); document.write( "

Algebra.Com's Answer #751437 by Boreal(15235) $\"\"$ $\"About$

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Original function has 4 sign changes so 4,2,0 positive roots
\n" ); document.write( "f(-x)=x^4-3x^3+2x^2-x+1 or no sign changes so 0 negative roots
\n" ); document.write( "rational roots can be factors of 1 divided by factors of 4
\n" ); document.write( "so they can be +/- 1, 1/2 and 1/4. But no negative roots, so they can be +1/4,1/2,1
\n" ); document.write( "look at 1 first since easiest to check
\n" ); document.write( "1
\n" ); document.write( " /4 -3 +2 -1 1
\n" ); document.write( "--4----1-----3----2----3 doesn't work (4-3+2-1+1 doesn't equal 0)
\n" ); document.write( "1/4
\n" ); document.write( " 4 -2 3/2 -1/4 15/16
\n" ); document.write( "1/2
\n" ); document.write( " 4 -1 -1/2 -5/4 doesn't work
\n" ); document.write( "There are 0 rational roots, 0 positive roots and the 4 roots are all complex (2 conjugate pairs.) The graph should not touch the x-axis. \r
\n" ); document.write( "\n" ); document.write( " $\"graph%28300%2C300%2C-10%2C10%2C-10%2C10%2C4x%5E4-3x%5E3%2B2x%5E2-x%2B1%29\"$ \n" ); document.write( "

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