document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1094145>Question 1094145</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For the quadratic equation 2x^2 + bx + 3 = 0, explain how to find a value of b where the discriminant yields a quadratic equation with the following types of solutions. <BR>\n" );
document.write( "A. two imaginary solutions<BR>\n" );
document.write( "B. one real solution<BR>\n" );
document.write( "C. two rational solutions<BR>\n" );
document.write( "D. two irrational solutions </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #708827 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=708827\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br>With the standard form of a quadratic equation<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "the discriminant<BR>\n" );
document.write( "<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;\" ><BR>\n" );
document.write( "in the quadratic formula determines which of these different cases you have.<br><BR>\n" );
document.write( "(1) If the discriminant is negative, there are no real solutions -- i.e., case A: two imaginary solutions.<BR>\n" );
document.write( "(2) If the discriminant is zero, there is a single real solution: case B.<BR>\n" );
document.write( "(3) If the discriminant is positive, then there are two real solutions.  Furthermore, the solutions are rational if the discriminant is a perfect square (case C), or they are irrational if the discriminant is not a perfect square (case D).<br><BR>\n" );
document.write( "With your quadratic, the discriminant is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4%282%29%283%29+=+b%5E2-24 ALIGN=MIDDLE  ALT=\"b%5E2-4%282%29%283%29+=+b%5E2-24\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "So you have...<BR>\n" );
document.write( "Case A, if b^2 is less than 24;<BR>\n" );
document.write( "Case B, if b^2 is equal to 24;<BR>\n" );
document.write( "Case C, if b^2-24 is a positive perfect square; and<BR>\n" );
document.write( "Case D, if b^2-24 is positive but not a perfect square. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );