document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=490686>Question 490686</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find a quadratic equation with roots -1+4i and -1-4i </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #334240 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</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=334240\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( " if you have the roots <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x1+=+-1%2B4i ALIGN=MIDDLE  ALT=\"x1+=+-1%2B4i\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x2+=+-1-4i ALIGN=MIDDLE  ALT=\"x2+=+-1-4i\"   DISABLED_style= \"max-width:90%; height:auto;\" > you can recover the quadratic equation by forming \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+%28-1%2B4i%29%29%28x+-%28+-1-4i%29%29=0 ALIGN=MIDDLE  ALT=\"%28x+-+%28-1%2B4i%29%29%28x+-%28+-1-4i%29%29=0\"   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=%28x+%2B1-4i%29%28x+%2B1%2B4i%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+%2B1-4i%29%28x+%2B1%2B4i%29+=+0\"   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=x%5E2%2Bx%2Bcross%284ix%29%2Bx+%2B1%2Bcross%284i%29-cross%284ix%29-cross%284i%29-%2816i%5E2%29=0 ALIGN=MIDDLE   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=x%5E2%2Bx%2Bx+%2B1-%2816%28-1%29%29=0 ALIGN=MIDDLE  ALT=\"x%5E2%2Bx%2Bx+%2B1-%2816%28-1%29%29=0\"   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=x%5E2%2B2x%2B1-%28-16%29=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B1-%28-16%29=0\"   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=x%5E2%2B2x%2B1%2B16=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B1%2B16=0\"   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=x%5E2%2B2x%2B17=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2x%2B17=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >.......your answer\r<BR>\n" );
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document.write( "check it:\r<BR>\n" );
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document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic_formula.solver>Quadratic Formula</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Let's use the quadratic formula to solve for x:<BR><BR>\n" );
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document.write( "  Starting with the general quadratic<BR>\n" );
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document.write( "  the general solution using the quadratic equation is:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  So lets solve <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B2%2Ax%2B17=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B2%2Ax%2B17=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=2 ALIGN=MIDDLE  ALT=\"b=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=17 ALIGN=MIDDLE  ALT=\"c=17\"   DISABLED_style= \"max-width:90%; height:auto;\" >)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%28+%282%29%5E2-4%2A1%2A17+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+%282%29%5E2-4%2A1%2A17+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=1, b=2, and c=17<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%28+4-4%2A1%2A17+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+4-4%2A1%2A17+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 2 to get 4  <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%28+4%2B-68+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+4%2B-68+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A17%2A1 ALIGN=MIDDLE  ALT=\"-4%2A17%2A1\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-68 ALIGN=MIDDLE  ALT=\"-68\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+sqrt%28+-64+%29%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+sqrt%28+-64+%29%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Combine like terms in the radicand (everything under the square root)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+8%2Ai%29%2F%282%2A1%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+8%2Ai%29%2F%282%2A1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplify the square root (note: If you need help with simplifying the square root, check out this <a  rel=nofollow HREF=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>)<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-2+%2B-+8%2Ai%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%28-2+%2B-+8%2Ai%29%2F%282%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 1 to get 2<BR>\n" );
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document.write( "  After simplifying, the quadratic has roots of<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1%2B4%2Ai ALIGN=MIDDLE  ALT=\"x=-1%2B4%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-1-4%2Ai ALIGN=MIDDLE  ALT=\"x=-1-4%2Ai\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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