document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=963221>Question 963221</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the cubic wquation that has -1 adn 2i as roots. Choices<BR>\n" );
document.write( "a)y=x cubed - x squared + 4x - 4<BR>\n" );
document.write( "b)y=x cubed + x squared - 4x - 4<BR>\n" );
document.write( "c)y=x cubed + x squared + 4x + 1<BR>\n" );
document.write( "d)y=x cubed + x squared + 4x + 4<BR>\n" );
document.write( "e)y=x cubed - x squared + 4x - 1\r<BR>\n" );
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document.write( "The book says the answer is D, but I do not understand the steps to get there.   </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #588457 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=588457\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "the cubic equation that has <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D=-1 ALIGN=MIDDLE  ALT=\"x%5B1%5D=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D=2i ALIGN=MIDDLE  ALT=\"x%5B2%5D=2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > as roots, have also <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B3%5D=-2i ALIGN=MIDDLE  ALT=\"x%5B3%5D=-2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > because complex root come always in pairs\r<BR>\n" );
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document.write( "now, since we have all roots, we can use zero product rule to see which cubic equation  is right answer\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29 ALIGN=MIDDLE  ALT=\"y=%28x-x%5B1%5D%29%28x-x%5B2%5D%29%28x-x%5B3%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x-%28-1%29%29%28x-2i%29%28x-%28-2i%29%29 ALIGN=MIDDLE  ALT=\"y=%28x-%28-1%29%29%28x-2i%29%28x-%28-2i%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B1%29%28x-2i%29%28x%2B2i%29 ALIGN=MIDDLE  ALT=\"y=%28x%2B1%29%28x-2i%29%28x%2B2i%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B1%29%28x%5E2-%282i%29%5E2%29 ALIGN=MIDDLE  ALT=\"y=%28x%2B1%29%28x%5E2-%282i%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B1%29%28x%5E2-%284i%5E2%29%29 ALIGN=MIDDLE  ALT=\"y=%28x%2B1%29%28x%5E2-%284i%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B1%29%28x%5E2-%284%28-1%29%29%29 ALIGN=MIDDLE  ALT=\"y=%28x%2B1%29%28x%5E2-%284%28-1%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B1%29%28x%5E2-%28-4%29%29 ALIGN=MIDDLE  ALT=\"y=%28x%2B1%29%28x%5E2-%28-4%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=%28x%2B1%29%28x%5E2%2B4%29 ALIGN=MIDDLE  ALT=\"y=%28x%2B1%29%28x%5E2%2B4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E3%2B4x%2Bx%5E2%2B4 ALIGN=MIDDLE  ALT=\"y=x%5E3%2B4x%2Bx%5E2%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E3%2Bx%5E2%2B4x%2B4 ALIGN=MIDDLE  ALT=\"y=x%5E3%2Bx%5E2%2B4x%2B4\"   DISABLED_style= \"max-width:90%; height:auto;\" >....=> so, answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D ALIGN=MIDDLE  ALT=\"D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "or, you can do it this way:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=x%5E3%2B+x%5E2+%2B+4x+%2B+4 ALIGN=MIDDLE  ALT=\"y=x%5E3%2B+x%5E2+%2B+4x+%2B+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >....to find zeros, set <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y=0 ALIGN=MIDDLE  ALT=\"y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and factor completely\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=%28x%5E3%2B+4x%29%2B+%28x%5E2++%2B+4%29 ALIGN=MIDDLE  ALT=\"0=%28x%5E3%2B+4x%29%2B+%28x%5E2++%2B+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0=x%28x%5E2%2B+4%29%2B+%28x%5E2++%2B+4%29 ALIGN=MIDDLE  ALT=\"0=x%28x%5E2%2B+4%29%2B+%28x%5E2++%2B+4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B+1%29+%28x%5E2++%2B+4%29=0 ALIGN=MIDDLE  ALT=\"%28x%2B+1%29+%28x%5E2++%2B+4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solutions:\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%2B+1%29 ALIGN=MIDDLE  ALT=\"%28x%2B+1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1 ALIGN=MIDDLE  ALT=\"x=-1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x%5E2++%2B+4%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2++%2B+4%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+=-+4 ALIGN=MIDDLE  ALT=\"x%5E2+=-+4\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=sqrt%28-4%29 ALIGN=MIDDLE  ALT=\"x=sqrt%28-4%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=2i ALIGN=MIDDLE  ALT=\"x=2i\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-2i ALIGN=MIDDLE  ALT=\"x=-2i\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "=> one more time we got that answer is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D ALIGN=MIDDLE  ALT=\"D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );