document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1091043>Question 1091043</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the solution the following quadratic equation<BR>\n" );
document.write( "X^2-12x+144=0<BR>\n" );
document.write( "X^2+3x-28=0 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #705519 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=705519\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The standard form of a quadratic function is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > where  <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2 ALIGN=MIDDLE  ALT=\"ax%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the quadratic term \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=bx ALIGN=MIDDLE  ALT=\"bx\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the linear term\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c ALIGN=MIDDLE  ALT=\"c\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the constant term\r<BR>\n" );
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document.write( "discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > tells us how many and what kind of roots quadratic function have <BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac%3E0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > quadratic function have two real roots<BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > quadratic function have one double root<BR>\n" );
document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac%3C0 ALIGN=MIDDLE  ALT=\"b%5E2-4ac%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > quadratic function have two complex roots\r<BR>\n" );
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document.write( "let check discriminant in your case \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-12x%2B144=0 ALIGN=MIDDLE  ALT=\"x%5E2-12x%2B144=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >...... <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-12%29%5E2-4%2A1%2A144 ALIGN=MIDDLE  ALT=\"%28-12%29%5E2-4%2A1%2A144\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=144-576 ALIGN=MIDDLE  ALT=\"144-576\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-432%3C0 ALIGN=MIDDLE  ALT=\"-432%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" >; so, your quadratic function will have have two complex roots\r<BR>\n" );
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document.write( "use quadratic formula to find roots: \r<BR>\n" );
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document.write( "1.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2-12x%2B144=0 ALIGN=MIDDLE  ALT=\"x%5E2-12x%2B144=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+=+%28-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%2A1%2A144+%29%29%2F%282%2A1%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%2A1%2A144+%29%29%2F%282%2A1%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=x+=+%2812+%2B-+sqrt%28+-432+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+sqrt%28+-432+%29%29%2F2+\"   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+=+%2812+%2B-+i%2Asqrt%28+432+%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+i%2Asqrt%28+432+%29%29%2F2+\"   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+=+%2812+%2B-+i%2A12+sqrt%283%29%29%2F2+ ALIGN=MIDDLE  ALT=\"x+=+%2812+%2B-+i%2A12+sqrt%283%29%29%2F2+\"   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+=+%28cross%2812%296+%2B-+i%2Across%2812%296+sqrt%283%29%29%2Fcross%282%29+ ALIGN=MIDDLE  ALT=\"x+=+%28cross%2812%296+%2B-+i%2Across%2812%296+sqrt%283%29%29%2Fcross%282%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=x+=+6+%2B+6i%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+6+%2B+6i%2Asqrt%283%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=x+=+6+-+6i%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"x+=+6+-+6i%2Asqrt%283%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=+graph%28+600%2C+600%2C+-10%2C+200%2C+-10%2C+200%2C+x%5E2-12x%2B144%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-10%2C+200%2C+-10%2C+200%2C+x%5E2-12x%2B144%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "2.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3x-28=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B3x-28=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "let check discriminant in this case:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%5E2-4%2A1%2A%28-28%29 ALIGN=MIDDLE  ALT=\"3%5E2-4%2A1%2A%28-28%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2B112 ALIGN=MIDDLE  ALT=\"9%2B112\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=121%3E0 ALIGN=MIDDLE  ALT=\"121%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" >; so, your quadratic function will have have two real roots\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B3x-28=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B3x-28=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >....factor completely\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2B7x-4x-28=0 ALIGN=MIDDLE  ALT=\"x%5E2%2B7x-4x-28=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%5E2%2B7x%29-%284x%2B28%29=0 ALIGN=MIDDLE  ALT=\"%28x%5E2%2B7x%29-%284x%2B28%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%28x%2B7%29-4%28x%2B7%29=0 ALIGN=MIDDLE  ALT=\"x%28x%2B7%29-4%28x%2B7%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+-+4%29+%28x+%2B+7%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+4%29+%28x+%2B+7%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+-+4%29++=+0 ALIGN=MIDDLE  ALT=\"%28x+-+4%29++=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=4 ALIGN=MIDDLE  ALT=\"x=4\"   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+%2B+7%29+=+0 ALIGN=MIDDLE  ALT=\"+%28x+%2B+7%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-7 ALIGN=MIDDLE  ALT=\"x=-7\"   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=+graph%28+600%2C+600%2C+-30%2C+30%2C+-30%2C+30%2C+x%5E2%2B3x-28%29+ ALIGN=MIDDLE  ALT=\"+graph%28+600%2C+600%2C+-30%2C+30%2C+-30%2C+30%2C+x%5E2%2B3x-28%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );