document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=193381>Question 193381</A>: <I><SPAN STYLE=\"word-break: break-all;\"> I couldn't work letter C and #2, please assist.\r<BR>\n" );
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document.write( "Please check the rest of the work and let me know if it is correct. \r<BR>\n" );
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document.write( "Solutions of Quadratic Equations and their Applications \r<BR>\n" );
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document.write( "1.	Determine whether the following equations have a real or complex solution.  Justify your answer. <BR>\n" );
document.write( "a)	x2 + 3x - 15 = 0 <BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = 3<BR>\n" );
document.write( "c = -15<BR>\n" );
document.write( "Discriminant: b2-4ac = 3 2-4*1*(-15) = 69<BR>\n" );
document.write( "Discriminant (69) is greater than zero. The equation has two solutions\r<BR>\n" );
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document.write( "b)	x2 + x + 4 = 0<BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = 1<BR>\n" );
document.write( "c = 4<BR>\n" );
document.write( "Discriminant: b2-4ac = 1 2-4*1*4 = -15 <BR>\n" );
document.write( "Discriminant (-15) is less than zero. No solutions are defined.\r<BR>\n" );
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document.write( "c)	  \r<BR>\n" );
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document.write( "d)	x2 – 8x + 16 = 0 \r<BR>\n" );
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document.write( "a = 1<BR>\n" );
document.write( "b = -8<BR>\n" );
document.write( "c = 16<BR>\n" );
document.write( "Discriminant: b2-4ac = 8 2-4*1*16 = 0 <BR>\n" );
document.write( "Discriminant (0) is zero. There is only one solution.\r<BR>\n" );
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document.write( "e)	2x2 - 3x + 7 = 0 <BR>\n" );
document.write( "b = -3<BR>\n" );
document.write( "c = 7 <BR>\n" );
document.write( "Discriminant: b2-4ac = 3 2-4*2*7 = -47<BR>\n" );
document.write( "Discriminant (-47) is less than zero. No solutions are defined.\r<BR>\n" );
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document.write( "f)	x2 – 4x - 77 = 0 <BR>\n" );
document.write( "a = 1<BR>\n" );
document.write( "b = -4<BR>\n" );
document.write( "c = -77<BR>\n" );
document.write( "Discriminant: b2-4ac = 4 2+4*1*(-77) = 324 <BR>\n" );
document.write( "Discriminant (324) is greater than zero. The equation has two solutions\r<BR>\n" );
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document.write( "g)	3x2 - 7x + 6 = 0<BR>\n" );
document.write( "a = 3<BR>\n" );
document.write( "b = -7<BR>\n" );
document.write( "c = 6<BR>\n" );
document.write( "Discriminant: b2-4ac = 7 2-4*3*6 = -23 <BR>\n" );
document.write( "Discriminant (-23) is less than zero. No solutions are defined.\r<BR>\n" );
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document.write( "h)	4x2 + 16x + 16 = 0 <BR>\n" );
document.write( "a = 4x<BR>\n" );
document.write( "b = 16<BR>\n" );
document.write( "c = 16<BR>\n" );
document.write( "Discriminant: b2-4ac = 16 2-4*4*16 = 0 <BR>\n" );
document.write( "Discriminant (0) is zero. There is only one solution.<BR>\n" );
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document.write( "2.	Find an equation for which -3 and 4 are solutions.\r<BR>\n" );
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document.write( "3.	What type of solution do you get for quadratic equations where D < 0? Give reasons for your answer. Also provide an example of such a quadratic equation and find the solution of the equation. \r<BR>\n" );
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document.write( "You get complex solutions for b^2-4ac<0.  <BR>\n" );
document.write( "x^2 +4x +5 = 0<BR>\n" );
document.write( "x = [-4 +/-(16-20)^1/2]/2 = -2 +/-i  <BR>\n" );
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document.write( "4.	Create a real-life situation that fits the equation (x + 3)(x - 5) = 0 and express the situation as the same equation.\r<BR>\n" );
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document.write( "The length of a rectangular field is 2 feet more than the width and the area of the field is 15 sq feet.<BR>\n" );
document.write( "Here is how we arrived at the equation from real life situation -<BR>\n" );
document.write( "Let the length be x, then width = x-2, <BR>\n" );
document.write( "and area = length * width<BR>\n" );
document.write( "so. x(x-2) = 15<BR>\n" );
document.write( "so, x^2 - 2x -15 =0<BR>\n" );
document.write( "Factoring we get <BR>\n" );
document.write( "(x+3)(x - 5) = 0<BR>\n" );
document.write( "so, x=5 (as lenth has to be positive) <BR>\n" );
document.write( "hence width = 3 feet </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #145187 by </B><A HREF=/tutors/aboutme.mpl?userid=solver91311><B>solver91311(24713)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=solver91311><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=solver91311><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=145187\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font face=\"Garamond\" size=\"+2\">\r<BR>\n" );
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document.write( "1a. Correct.\r<BR>\n" );
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document.write( "1b. You calculated the discriminant correctly, but interpreted the results incorrectly.  You said that there are no defined solutions.  In fact, there are no <i>real number</i> solutions.  However, there is a conjugate pair of complex solutions -- see your answer to #3.  Even if your instructor wanted you to answer \"No solution\" to these, you should still say \"No real number solution\"\r<BR>\n" );
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document.write( "1c. Can't help you with this one.  You didn't include the problem.\r<BR>\n" );
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document.write( "1d. Almost correct.  You should say that there is one real number solution with a multiplicity of 2.\r<BR>\n" );
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document.write( "1e. Same answer as 1b.\r<BR>\n" );
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document.write( "1f. Correct.\r<BR>\n" );
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document.write( "1g. Same answer as 1b.\r<BR>\n" );
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document.write( "1h. Same answer as 1d.\r<BR>\n" );
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document.write( "2. If -3 and 4 are solutions, then <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x = -3 \ \ \Rightarrow\ \ x + 3 = 0\"> and <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE x = 4 \ \ \Rightarrow\ \ x - 4 = 0\"> are the factors of the quadratic trinomial, so:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE \ \ \ \ \ \ \ \ \ \ (x + 3)(x - 4) = x^2 - x - 12 = 0\">\r<BR>\n" );
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document.write( "3.  Correct\r<BR>\n" );
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document.write( "4.  Correct\r<BR>\n" );
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document.write( "John<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\LARGE e^{i\pi} + 1 = 0\"><BR>\n" );
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