document.write( "Question 979438: How do i find the zeros of this equation \"+6x%5E3%2B5x%5E2-9x%2B2+\" \r
\n" ); document.write( "\n" ); document.write( "I have tried to factor out an x and than factor it as i would with
\n" ); document.write( "a normal quadratic but i reached this answer \"+-5%2Bsqrt%28193%29+%2F+12+\" and
\n" ); document.write( "\"-5-sqrt%28193%29+%2F+12+\" and i needed to multiply the x back in but i
\n" ); document.write( "did not know how to or what i should do after that. also because this is a
\n" ); document.write( "3rd degree polynomial than shouldn't it have 3 zeros. if possible please
\n" ); document.write( "show me step by step how to do this , thank you so much
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Algebra.Com's Answer #600703 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
If \"+6x%5E3%2B5x%5E2-9x%2B2+\" has a rational zero,
\n" ); document.write( "you should be able to use it to factor the polynomial,
\n" ); document.write( "and find the exact value of all of its real zeros.\r
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\n" ); document.write( "\n" ); document.write( "If \"+6x%5E3%2B5x%5E2-9x%2B2+\" does not have a rational zero,
\n" ); document.write( "you could only find approximate values by guided trial and error.\r
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\n" ); document.write( "\n" ); document.write( "If \"+6x%5E3%2B5x%5E2-9x%2B2+\" has a rational zero \"m%2Fn\" , it must be that
\n" ); document.write( "\"m\" is a factor of the constant term \"2\" , and
\n" ); document.write( "\"n\" is a factor of the leading coefficient \"6\" .
\n" ); document.write( "Factors of \"2\" are \"1\" , and \"2\" .
\n" ); document.write( "Factors of \"6\" are \"1\" , \"2\" , \"3\" , and \"6\" .
\n" ); document.write( "The possible values for \"m%2Fn\" are
\n" ); document.write( "-2, -1, -2/3, -1/3, -1/6, 1/6, 1/3, 2/3, 1, and 2.
\n" ); document.write( "You are expected to use synthetic division
\n" ); document.write( "(long division works too, but uses more ink)
\n" ); document.write( "to find that \"highlight%282%2F3%29\" is a zero.
\n" ); document.write( "(The other nine possible values are not zeros).
\n" ); document.write( "Synthetic division tells you
\n" ); document.write( "not only that \"6x%5E3%2B5x%5E2-9x%2B2\" is zero for \"x=2%2F3\" ,
\n" ); document.write( "but also that
\n" ); document.write( "\"%286x%5E3%2B5x%5E2-9x%2B2%29%2F%283x-2%29=2x%5E2%2B3x-1\"<--->\"6x%5E3%2B5x%5E2-9x%2B2%29=%283x-2%29%282x%5E2%2B3x-1%29\"
\n" ); document.write( "The other two zeros of \"6x%5E3%2B5x%5E2-9x%2B2\" are the zeros of \"2x%5E2%2B3x-1\" .
\n" ); document.write( "You can find if they are real zeros, and their value by solving
\n" ); document.write( "\"2x%5E2%2B3x-1=0\" .
\n" ); document.write( "You could do that by completing the square, or by applying
\n" ); document.write( "the quadratic formula \"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\" ,
\n" ); document.write( "which gives the solutions to \"ax%5E2%2Bbx%2Bc=0\"
\n" ); document.write( "In this case, with \"system%28a=2%2Cb=3%2Cc=-1%29\" , the solutions to \"2x%5E2%2B3x-1=0\" are
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