document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209115>Question 1209115</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Wilma and Greg were trying to solve the quadratic equation<BR>\n" );
document.write( "x^2 + bx + c = 0.<BR>\n" );
document.write( "Wilma wrote down the wrong value of b (but her value of c was correct), and found the roots to be 5 and 15.  Greg wrote down the wrong value of c (but his value of b was correct), and found the roots to be -5 and -7.  What are the actual roots of x^2 + bx + c = 0? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #847695 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=847695\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "If p,q are the roots then (x-p) and (x-q) are factors.<BR>\n" );
document.write( "We can then say (x-p)(x-q) = x^2+bx+c\r<BR>\n" );
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document.write( "Expand out the left hand side to get<BR>\n" );
document.write( "(x-p)(x-q) = x^2+bx+c<BR>\n" );
document.write( "x^2-qx-px+p*q = x^2+bx+c<BR>\n" );
document.write( "x^2-(p+q)x+p*q = x^2+bx+c\r<BR>\n" );
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document.write( "Compare terms<ul><li>The x coefficients on the left and right sides are -(p+q) and b respectively. Therefore b = -(p+q).</li><li>The constant terms on the left and right sides are p*q and c respectively. Therefore c = p*q.</li></ul>Side note: This is the quadratic case of <a  rel=nofollow HREF=\"https://mathworld.wolfram.com/VietasFormulas.html\">Vieta's Formulas</a>.\r<BR>\n" );
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document.write( "Wilma has the correct value of c, so,<BR>\n" );
document.write( "c = p*q = 5*15 = 75\r<BR>\n" );
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document.write( "Greg meanwhile has the correct value of b<BR>\n" );
document.write( "b = -(p+q) = -(-5 - 7) = 12\r<BR>\n" );
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document.write( "Therefore b = 12 and c = 75.<BR>\n" );
document.write( "The quadratic Wilma and Greg are trying to solve is x^2+12x+75 = 0.\r<BR>\n" );
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document.write( "I'll let the student take over from here.<BR>\n" );
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