document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1208474>Question 1208474</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is an unfactorable polynomial function: -4x^5-20x^4-23x^3+42x^2+20x-8.<BR>\n" );
document.write( "Can you please teach me how to solve for the x-intercepts manually without making the graph automatically using an app. I got 3 x-intercepts from the roots in the graph (-5.71..., 0.25..., 1.84...). Thank you so much. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846906 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52795)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=846906\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "This is an unfactorable polynomial function: -4x^5-20x^4-23x^3+42x^2+20x-8.\r<BR>\n" );
document.write( "\n" );
document.write( "Can you please teach me how to solve for the x-intercepts manually without <BR>\n" );
document.write( "making the graph automatically using an app. I got 3 x-intercepts from the roots <BR>\n" );
document.write( "in the graph (-5.71..., 0.25..., 1.84...). Thank you so much.<BR>\n" );
document.write( "~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This polynomial has no rational roots that can be found using Rational Root Test.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Solution\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "        <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D ALIGN=MIDDLE  ALT=\"x%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.27286,    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%7B2 ALIGN=MIDDLE  ALT=\"x%7B2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = −0.65098,    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D ALIGN=MIDDLE  ALT=\"x%5B3%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 1.08534,\r\n" );
document.write( "\r\n" );
document.write( "        <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B4%5D ALIGN=MIDDLE  ALT=\"x%5B4%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = −2.85361+1.49371i,    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%7B5%5D ALIGN=MIDDLE  ALT=\"x%7B5%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = −2.85361−1.49371i.\r\n" );
document.write( "​</PRE>\r<BR>\n" );
document.write( "\n" );
document.write( "Explanation\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This polynomial has no rational roots that can be found using Rational Root Test.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Roots were found using Newton method.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "An online solver was used from web-site \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "https://www.mathportal.org/calculators/solving-equations/polynomial-equation-solver.php\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "https://www.mathportal.org/calculators/solving-equations/polynomial-equation-solver.php?val1=-4x%5E5-20x%5E4-23x%5E3%2B42x%5E2%2B20x-8&val2=0&val3=-4%7Bx%7D%5E%7B5%7D-20%7Bx%7D%5E%7B4%7D-23%7Bx%7D%5E%7B3%7D%2B42%7Bx%7D%5E%7B2%7D%2B20x-8%3D0\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Notice that the found roots have nothing in common with the \"roots\" in your post,\r<BR>\n" );
document.write( "\n" );
document.write( "so, in this part, your post is a kind of disinformation.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "This equation does not allow factoring, does not allow to apply rational roots test and is of the degree 5.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Such algebraic/polynomial equations have no formulas to find their roots manually.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Only numerical solutions are possible, providing approximate values for the roots.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Did you get this assignment from your Math professor ? \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Math professor should know these basic truths as firmly as he (or she) knows that 2 x 2 = 4.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );