document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=355091>Question 355091</A>: <I><SPAN STYLE=\"word-break: break-all;\"> im really stuck on this question\r<BR>\n" );
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document.write( "the roots of the quadratic equation x^2 + 4x - a= 0 are b+1 and b-3. Find the values of a and b.<BR>\n" );
document.write( "thnks :) \r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #253613 by </B><A HREF=/tutors/aboutme.mpl?userid=jsmallt9><B>jsmallt9(3758)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jsmallt9><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=253613\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One form of a quadratic equation is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+r%5B1%5D%29%28x+-+r%5B2%5D%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+r%5B1%5D%29%28x+-+r%5B2%5D%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In this form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D ALIGN=MIDDLE  ALT=\"r%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B2%5D ALIGN=MIDDLE  ALT=\"r%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > are the two roots of the quadratic equation. This is the form which is often used when solving quadratic equations.<br><BR>\n" );
document.write( "So you equation, with its roots of b+1 and b-3, can be written in the form:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+%28b%2B1%29%29%28x+-+%28b-3%29%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+%28b%2B1%29%29%28x+-+%28b-3%29%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "which simplifies to:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x+-+b+-+1%29%28x+-+b+%2B+3%29+=+0 ALIGN=MIDDLE  ALT=\"%28x+-+b+-+1%29%28x+-+b+%2B+3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiplying this out (multiplying each term of one factor by each term of the other) we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-bx+%2B+3x+-bx+%2B+b%5E2+-3b+-x+%2Bb+-+3+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-bx+%2B+3x+-bx+%2B+b%5E2+-3b+-x+%2Bb+-+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Combining like terms we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-2bx+%2B+2x+%2B+b%5E2+-2b+-+3+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-2bx+%2B+2x+%2B+b%5E2+-2b+-+3+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then, for reasons that should be clear soon, I'll factor out the x from -2bx + 2x and also group the constant terms (the terms with no \"x\"):<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+%28-2b+%2B+2%29x+%2B+%28b%5E2+-2b+-+3%29+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+%28-2b+%2B+2%29x+%2B+%28b%5E2+-2b+-+3%29+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "In order for this equation to be the same as:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4x+-+a=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x+-+a=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "then the coefficients of the x terms must be the same:<BR>\n" );
document.write( "-2b + 2 = 4<BR>\n" );
document.write( "and the constant terms must be the same:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-2b+-+3+=+-a ALIGN=MIDDLE  ALT=\"b%5E2+-2b+-+3+=+-a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(The <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2 ALIGN=MIDDLE  ALT=\"x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > terms are already the same.) From<BR>\n" );
document.write( "-2b + 2 = 4<BR>\n" );
document.write( "we can solve for b:<BR>\n" );
document.write( "-2b = 2<BR>\n" );
document.write( "b = -1<BR>\n" );
document.write( "Then we can use this and the equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2+-2b+-+3+=+a ALIGN=MIDDLE  ALT=\"b%5E2+-2b+-+3+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" > to find a:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-1%29%5E2+-2%28-1%29+-+3+=+-a ALIGN=MIDDLE  ALT=\"%28-1%29%5E2+-2%28-1%29+-+3+=+-a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+-2%28-1%29+-+3+=+-a ALIGN=MIDDLE  ALT=\"1+-2%28-1%29+-+3+=+-a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%2B2+-+3+=+-a ALIGN=MIDDLE  ALT=\"1+%2B2+-+3+=+-a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+-a ALIGN=MIDDLE  ALT=\"0+=+-a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=0+=+a ALIGN=MIDDLE  ALT=\"0+=+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So a = 0 and b = -1 and your equation was <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+4x+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+4x+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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