document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=463547>Question 463547</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If 7x^2 + 4x = 3 , which of the following is (are) true?\r<BR>\n" );
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document.write( "I. The sum of the solutions is positive.<BR>\n" );
document.write( "II. The product of the solutions is negative.<BR>\n" );
document.write( "III. Both solutions are integers.\r<BR>\n" );
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document.write( "a) I only<BR>\n" );
document.write( "b) II only<BR>\n" );
document.write( "c) III only<BR>\n" );
document.write( "d) I and II only<BR>\n" );
document.write( "e) II and III only </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #317585 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=317585\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+7x%5E2+%2B+4x+=+3 ALIGN=MIDDLE  ALT=\"+7x%5E2+%2B+4x+=+3\"   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=+7x%5E2+%2B+4x+-+3=0 ALIGN=MIDDLE  ALT=\"+7x%5E2+%2B+4x+-+3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\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( "  <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;\" ><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=7%2Ax%5E2%2B4%2Ax-3=0 ALIGN=MIDDLE  ALT=\"7%2Ax%5E2%2B4%2Ax-3=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > ( notice <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=7 ALIGN=MIDDLE  ALT=\"a=7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=4 ALIGN=MIDDLE  ALT=\"b=4\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-3 ALIGN=MIDDLE  ALT=\"c=-3\"   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+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A7%2A-3+%29%29%2F%282%2A7%29 ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+%284%29%5E2-4%2A7%2A-3+%29%29%2F%282%2A7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in a=7, b=4, and c=-3<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B-+sqrt%28+16-4%2A7%2A-3+%29%29%2F%282%2A7%29 ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+16-4%2A7%2A-3+%29%29%2F%282%2A7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 4 to get 16  <BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B-+sqrt%28+16%2B84+%29%29%2F%282%2A7%29 ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+16%2B84+%29%29%2F%282%2A7%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-4%2A-3%2A7 ALIGN=MIDDLE  ALT=\"-4%2A-3%2A7\"   DISABLED_style= \"max-width:90%; height:auto;\" > to get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=84 ALIGN=MIDDLE  ALT=\"84\"   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+=+%28-4+%2B-+sqrt%28+100+%29%29%2F%282%2A7%29 ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+sqrt%28+100+%29%29%2F%282%2A7%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+=+%28-4+%2B-+10%29%2F%282%2A7%29 ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+10%29%2F%282%2A7%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+=+%28-4+%2B-+10%29%2F14 ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B-+10%29%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply 2 and 7 to get 14<BR>\n" );
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document.write( "  So now the expression breaks down into two parts<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+%2B+10%29%2F14 ALIGN=MIDDLE  ALT=\"x+=+%28-4+%2B+10%29%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-4+-+10%29%2F14 ALIGN=MIDDLE  ALT=\"x+=+%28-4+-+10%29%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Lets look at the first part:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-4+%2B+10%29%2F14 ALIGN=MIDDLE  ALT=\"x=%28-4+%2B+10%29%2F14\"   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=6%2F14 ALIGN=MIDDLE  ALT=\"x=6%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Add the terms in the numerator<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F7 ALIGN=MIDDLE  ALT=\"x=3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide<BR>\n" );
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document.write( "  So one answer is<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F7 ALIGN=MIDDLE  ALT=\"x=3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "  Now lets look at the second part:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=%28-4+-+10%29%2F14 ALIGN=MIDDLE  ALT=\"x=%28-4+-+10%29%2F14\"   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=-14%2F14 ALIGN=MIDDLE  ALT=\"x=-14%2F14\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract the terms in the numerator<BR>\n" );
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document.write( "  <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;\" > Divide<BR>\n" );
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document.write( "  So another answer is<BR>\n" );
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document.write( "  <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" );
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document.write( "  So our solutions are:<BR>\n" );
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document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F7 ALIGN=MIDDLE  ALT=\"x=3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <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" );
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document.write( "  </TD></TR>\n" );
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document.write( "so, solutions are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=3%2F7 ALIGN=MIDDLE  ALT=\"x=3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <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;\" >\r<BR>\n" );
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document.write( "check if\r<BR>\n" );
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document.write( "I. The sum of the solutions is positive.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2F7%2B%28-1%29=3%2F7-1=0.43-1=-0.57 ALIGN=MIDDLE  ALT=\"3%2F7%2B%28-1%29=3%2F7-1=0.43-1=-0.57\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "II. The product of the solutions is negative.\r<BR>\n" );
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document.write( "III. Both solutions are integers. \r<BR>\n" );
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document.write( "no, only one solution is integer\r<BR>\n" );
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document.write( "answer:\r<BR>\n" );
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document.write( "b) II only<BR>\n" );
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