document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=111671>Question 111671</A>: <I><SPAN STYLE=\"word-break: break-all;\"> please help me solve this<BR>\n" );
document.write( "a.calculate the value of the discriminant of x^2+x+3=0<BR>\n" );
document.write( "b.by examining the sign of the discriminant in part a, how many x-intercepts would the graph of y=x^2+x+3 have?why?<BR>\n" );
document.write( "this is under 1 problem. thank you tutor. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #81457 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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=81457\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Calculate the discriminant of:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+x%5E2%2Bx%2B3 ALIGN=MIDDLE  ALT=\"y+=+x%5E2%2Bx%2B3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Since this quadratic equation is already in the standard form of: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=y+=+ax%5E2%2Bbx%2Bc ALIGN=MIDDLE  ALT=\"y+=+ax%5E2%2Bbx%2Bc\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the discriminant is defined as: <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;\" >, then:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac+=+1%5E2-4%281%29%283%29 ALIGN=MIDDLE  ALT=\"b%5E2-4ac+=+1%5E2-4%281%29%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-12+=+-11 ALIGN=MIDDLE  ALT=\"1-12+=+-11\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "The discriminant is negative which means that the equation has two complex roots.<BR>\n" );
document.write( "Why, because the discriminant is the quantity under the radical (square root sign) and the square root of a negative number is an imaginary number, so that the roots will be complex.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-0.5%2Bsqrt%2811%29i ALIGN=MIDDLE  ALT=\"x+=+-0.5%2Bsqrt%2811%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+-0.5-sqrt%2811%29i ALIGN=MIDDLE  ALT=\"x+=+-0.5-sqrt%2811%29i\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Complex roots means that the graph of the equation (a parabola) never intercepts the x-axis, as shown by the graph below:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28600%2C400%2C-5%2C5%2C-5%2C5%2Cx%5E2%2Bx%2B3%29 ALIGN=MIDDLE  ALT=\"graph%28600%2C400%2C-5%2C5%2C-5%2C5%2Cx%5E2%2Bx%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );