document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=858686>Question 858686</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For which values of P will x^2+p+x=3(x+1) have real roots </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #517332 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=517332\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> your solution is in the attached picture.\r<BR>\n" );
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document.write( "number 1 takes your original equation and converts it to standard form of a quadratic equation.<BR>\n" );
document.write( "that form is ax^2 + bx + c = 0<BR>\n" );
document.write( "once the equation is transformed, you get:<BR>\n" );
document.write( "x^2 - 2x + (p-3) = 0 which results in:<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = -2<BR>\n" );
document.write( "c = (p - 3)\r<BR>\n" );
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document.write( "number 2 takes the discriminant from the quadratic formula that is used to perform the test to see if the roots are real or not.<BR>\n" );
document.write( "if the discriminant is not negative, then the roots are real.<BR>\n" );
document.write( "if the discriminant is negative, then the roots are not real.\r<BR>\n" );
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document.write( "the quadratic formula is:<BR>\n" );
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document.write( "             -b +/- sqrt(b^2-4ac)\r\n" );
document.write( "        x = -----------------------\r\n" );
document.write( "                    2a\r\n" );
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document.write( "the discriminant is the part that is under the square root sign.<BR>\n" );
document.write( "the discriminant is equal to b^2 - 4ac.<BR>\n" );
document.write( "if it is not negative the roots are real.<BR>\n" );
document.write( "if it is negative, the roots are not real.<BR>\n" );
document.write( "this is because the square root of a negative number is not real.\r<BR>\n" );
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document.write( "number 3 shows the discriminant equation that needs to be satisfied for the roots to be real.<BR>\n" );
document.write( "that equation is b^2 - 4ac >= 0\r<BR>\n" );
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document.write( "number 4 takes the equation from number 3 and replaces b with (-2) and replaces a with 1 and replaces c with (p - 3) and solves the equation of b^2 - 4ac >= 0<BR>\n" );
document.write( "the solution is that p must be smaller than or equal to 4 in order for the discriminant to be greater than or equal to 0.\r<BR>\n" );
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document.write( "number 5 takes the original equation of x^2 - 2x + (p - 3) = 0 and replaces p with 4 to see if the roots are real.<BR>\n" );
document.write( "they are real.<BR>\n" );
document.write( "this is good because 4 is smaller than or equal to 4 so the requirements are satisfied.\r<BR>\n" );
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document.write( "number 6 takes the original equation of x^2 - 2x + (p - 3) = 0 and replaces p with 3 to see if the roots are real.<BR>\n" );
document.write( "they are real.<BR>\n" );
document.write( "this is good because 3 is smaller than or equal to 4 so the requirements are again satisfied.\r<BR>\n" );
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document.write( "number 7 takes the original equation of x^2 - 2x + (p - 3) and replaces p with 5 to see if the roots are real.<BR>\n" );
document.write( "they are not real.<BR>\n" );
document.write( "this is good because 5 is not smaller than or equal to 4 so the requirements are again satisfied.\r<BR>\n" );
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document.write( "if p is smaller than or equal to 4, the roots are real.<BR>\n" );
document.write( "if p is not smaller than or equal to 4, the roots are not real.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/mar312.jpg\" alt=\"$$$\" </><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2014/mar313.jpg\" alt=\"$$$\" </><BR>\n" );
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