document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=549034>Question 549034</A>: <I><SPAN STYLE=\"word-break: break-all;\"> My daughter, has been having trouble working on her homework. Currently, 12:05 am and honestly. I don't know how to do any of these questions. Any help or examples of questions are greatly appreciated! MERRY CHIRSTMAS:)\r<BR>\n" );
document.write( "\n" );
document.write( "Find the complex zeros of the quadratic function.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%28x%29+=+x%5E2+-+12x+%2B+45 ALIGN=MIDDLE  ALT=\"h%28x%29+=+x%5E2+-+12x+%2B+45\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Without solving, determine the character of the solutions of the equation.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+-+2x+%2B+2+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+-+2x+%2B+2+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    Answer<BR>\n" );
document.write( "a. two unequal real solutions<BR>\n" );
document.write( "b. a repeated real solution<BR>\n" );
document.write( "c. two complex solutions that are conjugates of each other\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Find the x-intercept<BR>\n" );
document.write( "f(x) = -x2 + 7x - 12 \r<BR>\n" );
document.write( "\n" );
document.write( "Find the x-intercepts.<BR>\n" );
document.write( "f(x) = 2x^2 - 10x - 12\r<BR>\n" );
document.write( "\n" );
document.write( "Solve.<BR>\n" );
document.write( "x2 + 5 = 230<BR>\n" );
document.write( "      Answer<BR>\n" );
document.write( "±14<BR>\n" );
document.write( "15<BR>\n" );
document.write( "115<BR>\n" );
document.write( "±15\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Without solving, determine the character of the solutions of the equation.<BR>\n" );
document.write( "x2 + 7x + 6 = 0<BR>\n" );
document.write( "         Answer<BR>\n" );
document.write( "a. a repeated real solution<BR>\n" );
document.write( "b. two unequal real solutions<BR>\n" );
document.write( "c. two complex solutions that are conjugates of each other </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #357427 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=357427\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Find the complex zeros of the quadratic function.<BR>\n" );
document.write( "h(x) = x2 - 12x + 45<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=solve_quadratic_equation.solver>SOLVE quadratic equation (work shown, graph etc)</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-12x%2B45+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-12x%2B45+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-12%29%5E2-4%2A1%2A45=-36 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-12%29%5E2-4%2A1%2A45=-36\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  The discriminant -36 is less than zero. That means that there are no solutions among real numbers.<BR><BR>\n" );
document.write( "  If you are a student of advanced school algebra and are aware about <u>imaginary numbers<u>, read on.<BR><BR>\n" );
document.write( "  <BR>\n" );
document.write( "      In the field of imaginary numbers, the square root of -36 is + or - <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28+36%29+=+6 ALIGN=MIDDLE  ALT=\"sqrt%28+36%29+=+6\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "  <BR>\n" );
document.write( "      The solution is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28--12%2B-i%2Asqrt%28+-36+%29%29%2F2%5C1+=++%28--12%2B-i%2A6%29%2F2%5C1+ ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28--12%2B-i%2Asqrt%28+-36+%29%29%2F2%5C1+=++%28--12%2B-i%2A6%29%2F2%5C1+\"   DISABLED_style= \"max-width:90%; height:auto;\" >, or<BR>\n" );
document.write( "  Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-12%2Ax%2B45+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-12%2Ax%2B45+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );