document.write( "Question 164532This question is from textbook elementary and intermediate algebra
\n" ); document.write( ": I am having trouble getting started on these problems. Can someone please help?
\n" ); document.write( "Thank you in advance. Also, I may be making this too hard. Should I be factoring before I try to solve?
\n" ); document.write( "1. Determine whether the following equations have a solution or not? Justify your answer.
\n" ); document.write( "a) x2 + 6x - 7 = 0
\n" ); document.write( "b) z2 + z + 1 = 0
\n" ); document.write( "c) (3)1/2y2 - 4y - 7(3)1/2 = 0
\n" ); document.write( "d) 2x2 - 10x + 25 = 0
\n" ); document.write( "e) 2x2 - 6x + 5 = 0
\n" ); document.write( "f) s2 - 4s + 4 = 0
\n" ); document.write( "g) 5/6x2 - 7x - 6/5 = 0
\n" ); document.write( "h) 7a2 + 8a + 2 = 0 \r
\n" ); document.write( "\n" ); document.write( "2. If x = 1 and x = -8, then form a quadratic equation.
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Algebra.Com's Answer #121230 by jim_thompson5910(35256)\"\" \"About 
You can put this solution on YOUR website!
I'll do the first two to get you started\r
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\n" ); document.write( "\n" ); document.write( "For all of these problems, you need to use the discriminant formula \"D=b%5E2-4ac\" and you will get these possible solutions:\r
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\n" ); document.write( "\n" ); document.write( "If D>0 (ie the discriminant is positive), then you will have 2 real solutions,
\n" ); document.write( "If D=0, then you will have only 1 real solution, or
\n" ); document.write( "If D<0 (ie the discriminant is negative), then you will have 2 complex solutions (ie you will have NO real solutions). \r
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\n" ); document.write( "\n" ); document.write( "From \"x%5E2%2B6x-7\" we can see that \"a=1\", \"b=6\", and \"c=-7\"\r
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\n" ); document.write( "\n" ); document.write( "\"D=b%5E2-4ac\" Start with the discriminant formula.\r
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\n" ); document.write( "\n" ); document.write( "\"D=%286%29%5E2-4%281%29%28-7%29\" Plug in \"a=1\", \"b=6\", and \"c=-7\"\r
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\n" ); document.write( "\n" ); document.write( "\"D=36-4%281%29%28-7%29\" Square \"6\" to get \"36\"\r
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\n" ); document.write( "\n" ); document.write( "\"D=36--28\" Multiply \"4%281%29%28-7%29\" to get \"%284%29%28-7%29=-28\"\r
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\n" ); document.write( "\n" ); document.write( "\"D=36%2B28\" Rewrite \"D=36--28\" as \"D=36%2B28\"\r
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\n" ); document.write( "\n" ); document.write( "\"D=64\" Add \"36\" to \"28\" to get \"64\"\r
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\n" ); document.write( "\n" ); document.write( "Since the discriminant is greater than zero, this means that there are two real solutions.\r
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\n" ); document.write( "\n" ); document.write( "From \"z%5E2%2Bz%2B1\" we can see that \"a=1\", \"b=1\", and \"c=1\"\r
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\n" ); document.write( "\n" ); document.write( "\"D=b%5E2-4ac\" Start with the discriminant formula.\r
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\n" ); document.write( "\n" ); document.write( "\"D=%281%29%5E2-4%281%29%281%29\" Plug in \"a=1\", \"b=1\", and \"c=1\"\r
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\n" ); document.write( "\n" ); document.write( "\"D=1-4%281%29%281%29\" Square \"1\" to get \"1\"\r
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\n" ); document.write( "\n" ); document.write( "\"D=1-4\" Multiply \"4%281%29%281%29\" to get \"%284%29%281%29=4\"\r
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\n" ); document.write( "\n" ); document.write( "\"D=-3\" Subtract \"4\" from \"1\" to get \"-3\"\r
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\n" ); document.write( "\n" ); document.write( "Since the discriminant is less than zero, this means that there are two complex solutions. In other words, there are no real solutions.
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