document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=41895>Question 41895</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Use the value of discriminant to determine the number and type of roots for the equation 2x^2-7x+9=0.\r<BR>\n" );
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document.write( "Thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #27020 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=27020\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Comparing the given equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2x%5E2-7x%2B9=0 ALIGN=MIDDLE  ALT=\"2x%5E2-7x%2B9=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > with the standard 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;\" > we find a = 2, b = -7, c = 9.\r<BR>\n" );
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document.write( "The discriminant is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+b%5E2-4ac ALIGN=MIDDLE  ALT=\"D+=+b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Then if the coefficients i.e. a, b, c are real:<BR>\n" );
document.write( "1) If D > 0, the roots are real but unequal.<BR>\n" );
document.write( "2) If D = 0, the roots are real and equal.<BR>\n" );
document.write( "3) If D < 0, the roots are imaginery and conjugate.\r<BR>\n" );
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document.write( "Special case: <BR>\n" );
document.write( "If D > 0, D is a perfect square and the coefficients are also rational then the roots are also rational.\r<BR>\n" );
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document.write( "Here, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D+=+%28-7%29%5E2+-+4%2A2%2A9 ALIGN=MIDDLE  ALT=\"D+=+%28-7%29%5E2+-+4%2A2%2A9\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 49 - 72 = -23.<BR>\n" );
document.write( "Hence, D < 0, also the coefficients are real and so the roots are imaginery and conjugate.\r<BR>\n" );
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document.write( "For a brief discussion on rational numbers you may see my lesson at<BR>\n" );
document.write( "http://www.algebra.com/tutors/INTRODUCTION_TO_RATIONAL_AND_IRRATIONAL_NUMBERS.lesson?content_action=show_dev </SPAN>\n" );
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