document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=267203>Question 267203</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I am trying to help my child with her homework.  So, if you can explain it to me, maybe I can explain it to her.....without GIVING her the answer!\r<BR>\n" );
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document.write( "Find all of the zeros of the function:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29=x%5E4-15x%5E3%2B70x%5E2-70x-156 ALIGN=MIDDLE  ALT=\"h%28x%29=x%5E4-15x%5E3%2B70x%5E2-70x-156\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "I know how to figure out how many positive and negative zeros, but I don't understand how to figure out how many imaginary zeros.  Then I don't know how to find all of the zeros. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #196176 by </B><A HREF=/tutors/aboutme.mpl?userid=drk><B>drk(1908)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=drk><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=196176\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29=x%5E4-15x%5E3%2B70x%5E2-70x-156 ALIGN=MIDDLE  ALT=\"h%28x%29=x%5E4-15x%5E3%2B70x%5E2-70x-156\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "first we use a technique called P-N-I This gives us the positive negative and imaginary zero combinations<BR>\n" );
document.write( "P . . . N . . . I<BR>\n" );
document.write( "3 . . . 1 . . . 0<BR>\n" );
document.write( "1 . . . .1 . . . 2<BR>\n" );
document.write( "So, I see that we must have 1 negative root somewhere.<BR>\n" );
document.write( "Next I apply synthetic division to get roots.<BR>\n" );
document.write( "-1 // 1 . . . . -15 . . . . 70 . . . . -70 . . . . -156<BR>\n" );
document.write( " . . . . . . . . . . .-1 . . . . 16 . . . . .-86 . . . . 156<BR>\n" );
document.write( " . . . . .1 . . . . .-16 . . . 86 . . . . .-156 . . . .0<BR>\n" );
document.write( "and then<BR>\n" );
document.write( "6// 1 . . . . -16 . . . . 86 . . . . -156 <BR>\n" );
document.write( " . . . . . . . . . . 6 . . . . -60 . . . .156<BR>\n" );
document.write( " . . . . .1 . . . -10 . . . 26 . . . . .0<BR>\n" );
document.write( "So we know that -1 and 6 are roots.<BR>\n" );
document.write( "Now we can factor x^2 - 10x + 26 using the quadratic as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+sqrt%28+100-4%2A1%2A26+%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+sqrt%28+100-4%2A1%2A26+%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%2810+%2B-+sqrt%28-4%29%29%2F%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%2810+%2B-+sqrt%28-4%29%29%2F%282%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which gives us imaginary answers of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%285+%2B-+i%29+ ALIGN=MIDDLE  ALT=\"x+=+%285+%2B-+i%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "-----<BR>\n" );
document.write( "So, in total we have the following roots:<BR>\n" );
document.write( "-6, 6, and 5 +-i </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );