document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192005>Question 1192005</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the values of​ a, b, and c for which the quadratic equation ax^2+bx+c=0 has the solutions 5-√26 and 5+ √26.<BR>\n" );
document.write( "​(Hint: Use the​ zero-product property in​ reverse.)<BR>\n" );
document.write( "a=<BR>\n" );
document.write( "b=<BR>\n" );
document.write( "c=<BR>\n" );
document.write( "(Type an integer or a simplified faction.)<BR>\n" );
document.write( "Thank you so much for your help!(: </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #823890 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=823890\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "I'll use a different approach instead of the hint given. <BR>\n" );
document.write( "If you prefer the hint route, then let me know and I'll fix my solution.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5+-+sqrt%2826%29 ALIGN=MIDDLE  ALT=\"x+=+5+-+sqrt%2826%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5+%2B+sqrt%2826%29 ALIGN=MIDDLE  ALT=\"x+=+5+%2B+sqrt%2826%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the two given roots or x intercepts.\r<BR>\n" );
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document.write( "For each equation, subtract 5 from both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5+=+-sqrt%2826%29 ALIGN=MIDDLE  ALT=\"x-5+=+-sqrt%2826%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-5+=+sqrt%2826%29 ALIGN=MIDDLE  ALT=\"x-5+=+sqrt%2826%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "If we square both sides, then each right hand side yields 26. <BR>\n" );
document.write( "The squaring operation and square root cancel out.<BR>\n" );
document.write( "So we have this equation<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2+=+26 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2+=+26\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Let's get it into standard form ax^2+bx+c = 0<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-5%29%5E2+=+26 ALIGN=MIDDLE  ALT=\"%28x-5%29%5E2+=+26\"   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-5%29%28x-5%29+=+26 ALIGN=MIDDLE  ALT=\"%28x-5%29%28x-5%29+=+26\"   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-5%29-5%28x-5%29+=+26 ALIGN=MIDDLE  ALT=\"x%28x-5%29-5%28x-5%29+=+26\"   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%5E2-5x-5x%2B25+=+26 ALIGN=MIDDLE  ALT=\"x%5E2-5x-5x%2B25+=+26\"   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%5E2-5x-5x%2B25-26=0 ALIGN=MIDDLE  ALT=\"x%5E2-5x-5x%2B25-26=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%5E2-10x-1=0 ALIGN=MIDDLE  ALT=\"x%5E2-10x-1=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Comparing this to ax^2+bx+c = 0, we have<BR>\n" );
document.write( "<font color=red>a = 1<BR>\n" );
document.write( "b = -10<BR>\n" );
document.write( "c = -1<BR>\n" );
document.write( "</font>\r<BR>\n" );
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document.write( "To verify the answers, let's use the quadratic formula to plug in those a,b,c values<BR>\n" );
document.write( "We should get the roots your teacher gave you<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29 ALIGN=MIDDLE  ALT=\"x+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%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+=+%28-%28-10%29%2B-sqrt%28%28-10%29%5E2-4%281%29%28-1%29%29%29%2F%282%281%29%29 ALIGN=MIDDLE  ALT=\"x+=+%28-%28-10%29%2B-sqrt%28%28-10%29%5E2-4%281%29%28-1%29%29%29%2F%282%281%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=x+=+%2810%2B-sqrt%28100%2B4%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2810%2B-sqrt%28100%2B4%29%29%2F%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+=+%2810%2B-sqrt%28104%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2810%2B-sqrt%28104%29%29%2F%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+=+%2810%2B-sqrt%284%2A26%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2810%2B-sqrt%284%2A26%29%29%2F%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+=+%2810%2B-sqrt%284%29%2Asqrt%2826%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2810%2B-sqrt%284%29%2Asqrt%2826%29%29%2F%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+=+%2810%2B-++++2%2Asqrt%2826%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%2810%2B-++++2%2Asqrt%2826%29%29%2F%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+=+%282%285%2B-sqrt%2826%29%29%29%2F%282%29 ALIGN=MIDDLE  ALT=\"x+=+%282%285%2B-sqrt%2826%29%29%29%2F%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+=+5%2B-sqrt%2826%29 ALIGN=MIDDLE  ALT=\"x+=+5%2B-sqrt%2826%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+=+5%2Bsqrt%2826%29 ALIGN=MIDDLE  ALT=\"x+=+5%2Bsqrt%2826%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > or <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+5-sqrt%2826%29 ALIGN=MIDDLE  ALT=\"x+=+5-sqrt%2826%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "We've confirmed the answers.\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "<font color=red>a = 1<BR>\n" );
document.write( "b = -10<BR>\n" );
document.write( "c = -1<BR>\n" );
document.write( "</font><BR>\n" );
document.write( "</font> </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );