document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=205728>Question 205728</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0395145074/algebrahomeworkh>Book 1 Modern Algebra Structure and Method</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> 12. Given the quadratic equation: X(to the 2nd power) -5X +1 = 0<BR>\n" );
document.write( "a. what is the sum of the roots?<BR>\n" );
document.write( "b. What is the product of the roots?\r<BR>\n" );
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document.write( "13.  Write a quadratic equation such that the sum of the roots is 6 and the product of the roots is -11.\r<BR>\n" );
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document.write( "14, One number is 14 more than another number. Their product is 351. What are the numbers.\r<BR>\n" );
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document.write( "Thank you very much...please help me! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #155457 by </B><A HREF=/tutors/aboutme.mpl?userid=RAY100><B>RAY100(1637)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=RAY100><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=155457\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> x^2 -5x +1<BR>\n" );
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document.write( "solve for  roots  using  quadratic  eqn<BR>\n" );
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document.write( "a=1,,,,b=(-5),,,,,c=1<BR>\n" );
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document.write( "x= [-(-5) +/- sqrt{(-5)^2 -4(1)(1)}] / 2(1)<BR>\n" );
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document.write( "x=[ 5+/- sqrt{25-4}]/2<BR>\n" );
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document.write( "x=[ 5+/- 4.583}/2<BR>\n" );
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document.write( "x= 4.79,,,.209<BR>\n" );
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document.write( "a) sum = 4.79 +.209 = 5<BR>\n" );
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document.write( "b) product = (4.79)(.209) =1<BR>\n" );
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document.write( "(13) (1) x + y =6,,,,,,x=6-y<BR>\n" );
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document.write( "(2) xy = -11<BR>\n" );
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document.write( "substitute  in (2)   (6-y)(y) - -11<BR>\n" );
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document.write( "6y -y^2 =-11<BR>\n" );
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document.write( "y^2 -6y -11 =0<BR>\n" );
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document.write( "check,  solving  using  quadratic  eqn, y= 7.472, -1.472,,,<BR>\n" );
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document.write( "7.472 -1.472 =6,,,ok,,,,,,,,,,,,,7.472*-1.472 = -11,,,ok<BR>\n" );
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document.write( "14),,(1) x=y+14<BR>\n" );
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document.write( "(2) xy = 351<BR>\n" );
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document.write( "substitute  (1) into (2)<BR>\n" );
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document.write( "(y+14)(y) =351<BR>\n" );
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document.write( "y^2 +14y -351 =0<BR>\n" );
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document.write( "(y+27)(y-13) =0<BR>\n" );
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document.write( "y= -27,,,+13,,,,,,,,x= -13, 27<BR>\n" );
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document.write( "solutions (27,13),,,(-13,-27)<BR>\n" );
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document.write( "check,,,,27 = 13+14,,,ok,,,,27*13 = 351<BR>\n" );
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document.write( "-13 = -27 +14,,,ok,,,,,,,,,,-13*-27 = +351,,,,ok<BR>\n" );
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document.write( " </SPAN>\n" );
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