document.write( "Question 644950: Find all real zeros of the function:
\n" ); document.write( "h(x)= x^5+15x^4+72x^3+80x^2-225x-375 \n" ); document.write( "
Algebra.Com's Answer #405338 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
Find all real zeros of the function:
\n" ); document.write( "h(x)= x^5+15x^4+72x^3+80x^2-225x-375
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\n" ); document.write( "Use the rational roots theorem to solve:\r
\n" ); document.write( "\n" ); document.write( "....0...|....1......15......72.....80......-225......-375.............
\n" ); document.write( "....1...|....1......16......88.....168.....-57.......-432
\n" ); document.write( "...,2...|....1......17.....194....468.....711.......1047 (zero exists between 1 and 2)
\n" ); document.write( "....3...|....1......18.....126....458.....1149.....3072 (3 is upper boundary)
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\n" ); document.write( "..-1...|....1......14.....58.......22.....-247.....-128
\n" ); document.write( "..-2...|....1......13.....46.....-12.....-201.......27 (zero exists between -1 and -2)
\n" ); document.write( "..-3...|....1......12.....36.....-28.....-141......48
\n" ); document.write( "..-4...|....1......11.....28.....-32.....-119......101
\n" ); document.write( "..-5...|....1......10.....22.....-30.....-75..........0 (-5 is a root)
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\n" ); document.write( "..-5...|....1......5.......-3......-15......0 (-5 is a root of multiplicity 2)
\n" ); document.write( "h(x)=(x+5)(x+5)(x^3+5x^2-3x-15)
\n" ); document.write( "h(x)=(x+5)(x+5)(x^2(x+5)-3(x+5)
\n" ); document.write( "h(x)=(x+5)(x+5)(x^2-3)(x+5)
\n" ); document.write( "The 5 zeros are: -5 (multiplicity 3), √3 and -√3
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\n" ); document.write( "note: I had the help of a graphic computer program to check my answers.\r
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