document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=172100>Question 172100</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.	Determine whether the following equations have a solution or not? Justify your answer. <BR>\n" );
document.write( "a)	x2 + 6x - 7 = 0 <BR>\n" );
document.write( "b)	z2 + z + 1 = 0<BR>\n" );
document.write( "c)	 (3)1/2y2 - 4y - 7(3)1/2 = 0 <BR>\n" );
document.write( "d)	2x2 - 10x + 25 = 0 <BR>\n" );
document.write( "e)	2x2 - 6x + 5 = 0 <BR>\n" );
document.write( "f)	s2 - 4s + 4 = 0 <BR>\n" );
document.write( "g)	5/6x2 - 7x - 6/5 = 0<BR>\n" );
document.write( "h)	7a2 + 8a + 2 = 0 <BR>\n" );
document.write( "2.	If x = 1 and x = -8, then form a quadratic equation. <BR>\n" );
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. <BR>\n" );
document.write( "4. Create a real-life situation that fits into the equation (x + 4)(x - 7) = 0 and express the situation as the same equation. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #127162 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=127162\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1.  In the first place, ALL quadratic equations have two roots -- The Fundamental Theorem of Algebra says so.  The question is, are the roots real numbers or not.  Use the discriminant to make the determination.\r<BR>\n" );
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document.write( "The discriminant is the part of the quadratic formula that is under the radical sign.\r<BR>\n" );
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document.write( "Quadratic formula:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ ALIGN=MIDDLE  ALT=\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "So the discriminant is:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DELTA+=+b%5E2-4ac ALIGN=MIDDLE  ALT=\"DELTA+=+b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Use the discriminant to determine the character of the roots of a quadratic equation.\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DELTA=0 ALIGN=MIDDLE  ALT=\"DELTA=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > there is one real number root with a multiplicity of 2.\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DELTA%3E0 ALIGN=MIDDLE  ALT=\"DELTA%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > there are two real number roots.\r<BR>\n" );
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document.write( "if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DELTA%3C0 ALIGN=MIDDLE  ALT=\"DELTA%3C0\"   DISABLED_style= \"max-width:90%; height:auto;\" > there is a conjugate pair of complex roots of the form <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2B-bi ALIGN=MIDDLE  ALT=\"a%2B-bi\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "I'll do the first one, and then you can do the rest:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2+%2B+6x+-+7+=+0 ALIGN=MIDDLE  ALT=\"x%5E2+%2B+6x+-+7+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Here, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a=1 ALIGN=MIDDLE  ALT=\"a=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b=6 ALIGN=MIDDLE  ALT=\"b=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=-7 ALIGN=MIDDLE  ALT=\"c=-7\"   DISABLED_style= \"max-width:90%; height:auto;\" >, so <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=DELTA=6%5E2-4%281%29%28-7%29=36%2B28=64%3E0 ALIGN=MIDDLE  ALT=\"DELTA=6%5E2-4%281%29%28-7%29=36%2B28=64%3E0\"   DISABLED_style= \"max-width:90%; height:auto;\" > so there are two real number roots.\r<BR>\n" );
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document.write( "Simple as that.  You can do the rest.\r<BR>\n" );
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document.write( "2.  To be exactly correct, this problem is incorrectly stated.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > cannot simultaneously be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1 ALIGN=MIDDLE  ALT=\"1\"   DISABLED_style= \"max-width:90%; height:auto;\" > AND <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=-8 ALIGN=MIDDLE  ALT=\"-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <b>OR</b> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-8 ALIGN=MIDDLE  ALT=\"x=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Here's the rule:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a root of a polynomial equation if and only if <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-a ALIGN=MIDDLE  ALT=\"x-a\"   DISABLED_style= \"max-width:90%; height:auto;\" > is a factor of the polynomial.\r<BR>\n" );
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document.write( "Since <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=1 ALIGN=MIDDLE  ALT=\"x=1\"   DISABLED_style= \"max-width:90%; height:auto;\" > <b>OR</b> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=-8 ALIGN=MIDDLE  ALT=\"x=-8\"   DISABLED_style= \"max-width:90%; height:auto;\" > are roots of the desired quadratic, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x-1 ALIGN=MIDDLE  ALT=\"x-1\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%2B8 ALIGN=MIDDLE  ALT=\"x%2B8\"   DISABLED_style= \"max-width:90%; height:auto;\" > must be factors of the quadratic polynomial, so just multiply <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-1%29%28x%2B8%29 ALIGN=MIDDLE  ALT=\"%28x-1%29%28x%2B8%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and set the result equal to zero.\r<BR>\n" );
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document.write( "3.  This one is answered in the discussion for problem 1 above.\r<BR>\n" );
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document.write( "4.  No idea how to answer this one.  You get zeros at -4 and 7, and a minimum value at 1.5  Your guess is as good as mine. </SPAN>\n" );
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