document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=961545>Question 961545</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The question is to find all quadratic equations with roots 2+3i and 2-3i. I have actually been given an answer by my teacher, but I wish to find out the logic behind this. My teacher has given me a solution, which is found below. <BR>\n" );
document.write( "sum=4=-b/a<BR>\n" );
document.write( "Product=4+9=13=c/a<BR>\n" );
document.write( "=> a=1, b=-4, c=13<BR>\n" );
document.write( "a(x^2-4x+13)=0<BR>\n" );
document.write( "So, there it is. I understand how to perform sums like this with square roots and normal integers in the place of i, but I do not understand where to even start with i in the equation, as I have tried the usual method that I use for numbers and roots and the answer I received was incorrect. Any help would be much appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #587533 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=587533\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The question is to find all quadratic equations with roots 2+3i and 2-3i. I have actually been given an answer by my teacher, but I wish to find out the logic behind this. My teacher has given me a solution, which is found below. <BR>\n" );
document.write( "sum=4=-b/a<BR>\n" );
document.write( " Product=4+9=13=c/a<BR>\n" );
document.write( " => a=1, b=-4, c=13<BR>\n" );
document.write( " a(x^2-4x+13)=0<BR>\n" );
document.write( " So, there it is. I understand how to perform sums like this with square roots and normal integers in the place of i, but I do not understand where to even start with i in the equation, as I have tried the usual method that I use for numbers and roots and the answer I received was incorrect. Any help would be much appreciated.<BR>\n" );
document.write( "---------------------<BR>\n" );
document.write( "Form:: y = ax^2+bx+c<BR>\n" );
document.write( "Roots:: x = [-b+sqrt(b^2-4ac)]/(2a) and x = [-b-sqrt(b^2-4ac)]/(2a)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Adding them you get: 2(-b/(2a)) = -b/a<BR>\n" );
document.write( "Multiplying them you get: (-b/(2a))^2-(sqrt(b^2-4ac))^2/(2a)^2) <BR>\n" );
document.write( "= (b^2/4a^2 - (b^2-4ac))/(4a^2)<BR>\n" );
document.write( "= (b^2 - b^2 + 4ac)/(4a^2) = 4ac/(4a^2) = c/a<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "Your roots are 2+3i and 2-3i<BR>\n" );
document.write( "Sum = 4, so -b/a = 4 or -b = 4a<BR>\n" );
document.write( "Product = 4+9 = 13, So c/a = 13 or c = 13a<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "y = ax^2 -4ax + 13a<BR>\n" );
document.write( "---<BR>\n" );
document.write( "y = a(x^2 - 4x + 13)<BR>\n" );
document.write( "------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "============== </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );