document.write( "Question 1042655: Please help me solve this equation
\n" ); document.write( "1. Solve the following inequality for x:
\n" ); document.write( "3x^2 - 8x > 3\r
\n" ); document.write( "\n" ); document.write( "2. Without solving the equation 3x^2 - 8x -3 = 0
\n" ); document.write( "Show that it has two different rational roots.\r
\n" ); document.write( "\n" ); document.write( "Thanks for your help... \n" ); document.write( "
Algebra.Com's Answer #657684 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
Please help me solve this equation
\n" ); document.write( "1. Solve the following inequality for x:
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\r\n" );
document.write( "     3x²-8x > 3\r\n" );
document.write( "   3x²-8x-3 > 0\r\n" );
document.write( "(x-3)(3x+1) > 0\r\n" );
document.write( "Critical numbers are the zeroes of\r\n" );
document.write( "the factors, 3, -1/3.\r\n" );
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document.write( "We graph the critical numbers on a number line.\r\n" );
document.write( "Since the inequality symbols are > and not \"%22%22%3E=%22%22\",\r\n" );
document.write( "the critical numbers cannot be solutions, so we draw \r\n" );
document.write( "open circles at each critical number.\r\n" );
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document.write( "-----------o--------------------o-----------\r\n" );
document.write( "-2    -1 \"-1%2F3\" 0     1     2     3     4     5\r\n" );
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document.write( "We test each interval.\r\n" );
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document.write( "We pick a test point on \"%28matrix%281%2C3%2C-infinity%2C%22%2C%22%2C-1%2F3%29%29\"\r\n" );
document.write( "We pick -1 and substitute it in\r\n" );
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document.write( "   (x-3)(3x+1) > 0\r\n" );
document.write( "  (-1-3)(3∙-1+1) > 0\r\n" );
document.write( "    (-4)(-3+1) > 0\r\n" );
document.write( "      (-4)(-2) > 0\r\n" );
document.write( "             8 > 0\r\n" );
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document.write( "That's true so we shade that interval on\r\n" );
document.write( "the number line:\r\n" );
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document.write( "<==========o--------------------o-----------\r\n" );
document.write( "-2    -1 \"-1%2F3\" 0     1     2     3     4     5  \r\n" );
document.write( "Show that it has two different rational roots.\r\n" );
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document.write( "Next we pick a test point on \"%28matrix%281%2C3%2C-1%2F3%2C%22%2C%22%2C3%29%29\"\r\n" );
document.write( "We pick 0 and substitute it in\r\n" );
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document.write( "   (x-3)(3x+1) > 0\r\n" );
document.write( "  (0-3)(3∙0+1) > 0\r\n" );
document.write( "       (-3)(1) > 0\r\n" );
document.write( "            -3 > 0\r\n" );
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document.write( "That's false so we DO NOT shade that interval on\r\n" );
document.write( "the number line.  We still have this:\r\n" );
document.write( "\r\n" );
document.write( "<==========o--------------------o-----------\r\n" );
document.write( "-2    -1 \"-1%2F3\" 0     1     2     3     4     5\r\n" );
document.write( "\r\n" );
document.write( "We test each interval.\r\n" );
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document.write( "We pick a test point on \"%28matrix%281%2C3%2C3%2C%22%2C%22%2Cinfinity%29%29\"\r\n" );
document.write( "We pick 4 and substitute it in\r\n" );
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document.write( "   (x-3)(3x+1) > 0\r\n" );
document.write( "(4-3)(3∙4+1) > 0\r\n" );
document.write( "     (1)(12+1) > 0\r\n" );
document.write( "       (1)(13) > 0\r\n" );
document.write( "            13 > 0\r\n" );
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document.write( "That's true so we shade that interval on\r\n" );
document.write( "the number line:\r\n" );
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document.write( "<==========o--------------------o==========>\r\n" );
document.write( "-2    -1 \"-1%2F3\" 0     1     2     3     4     5\r\n" );
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document.write( "So the solution in interval notation is\r\n" );
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document.write( "  \r\n" );
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document.write( "----------------\r\n" );
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\n" ); document.write( "2. Without solving the equation 3x² - 8x - 3 = 0
\n" ); document.write( "Show that it has two different rational roots.
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\r\n" );
document.write( "[That's funny for we already had to solve it to\r\n" );
document.write( "get the critical values in the first problem. :) ]\r\n" );
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document.write( "But pretending we hadn't, we would just show that\r\n" );
document.write( "the discriminant is a perfect square:\r\n" );
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document.write( "Discriminant = b²-4ac = (-8)²-4(3)(-3) = 64+36 = 100\r\n" );
document.write( "which is 10², a perfect square, so we know that the\r\n" );
document.write( "quadratic has two rational roots. \r\n" );
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document.write( "Edwin
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