document.write( "Question 1149716: Find the solution of the following polynomial inequality. Express your answer in interval notation.\r
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Algebra.Com's Answer #771064 by ikleyn(52847) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "For simplicity, multiply both sides of the given inequality by (-1). You will get then an EQUIVALENT inequality\r\n" );
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document.write( "    (x-4)*(x+2)*(x-3) < 0      (1)\r\n" );
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document.write( "The polynomial in the left side has simple roots  -2, 3 and 4, in ascending order.\r\n" );
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document.write( "Each root is of the multiplicity of 1.\r\n" );
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document.write( "It means that the values of polynomial are of the same sign in each particular interval between the neighbor roots\r\n" );
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document.write( "and change their signs when the variable \"x\" passes each of the roots.\r\n" );
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document.write( "With it in mind, it is VERY SIMPLE to solve the problem.\r\n" );
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document.write( "    In the interval  (-oo,-2) the polynomial (1) is negative;\r\n" );
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document.write( "    in the interval  (-2,3)   the polynomial (1) is positive;\r\n" );
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document.write( "    in the interval  (3,4)    the polynomial (1) is negative;\r\n" );
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document.write( "    in the interval  (4,oo)   the polynomial (1) is positive.\r\n" );
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document.write( "So, the solution to the given inequality is this union of two intervals  (-oo,-2) U (3,4).    \r\n" );
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\n" ); document.write( "\n" ); document.write( "If you want to see other similar solved problems, look into my lessons\r
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\n" ); document.write( "\n" ); document.write( "    - Solving problems on quadratic inequalities \r
\n" ); document.write( "\n" ); document.write( "    - Solving inequalities for high degree polynomials factored into a product of linear binomials \r
\n" ); document.write( "\n" ); document.write( "    - Solving inequalities for rational functions with numerator and denominator factored into a product of linear binomials \r
\n" ); document.write( "\n" ); document.write( "    - Solving inequalities for rational functions with non-zero right side \r
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\n" ); document.write( "\n" ); document.write( "and\r
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\n" ); document.write( "\n" ); document.write( "    - Domain of a function which is a quadratic polynomial under the square root operator \r
\n" ); document.write( "\n" ); document.write( "    - Domain of a function which is a high degree polynomial under the square root operator \r
\n" ); document.write( "\n" ); document.write( "    - Domain of a function which is the square root of a rational function.\r
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\n" ); document.write( "Comment from student: Thanks a lot Ikleyn. What is the link of your website? I can share.
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\n" ); document.write( "\n" ); document.write( "My response :   This forum is constructed in the way that i CAN NOT identify from whom I got the message/(the \"comment\").\r
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\n" ); document.write( "\n" ); document.write( "Therefore, when I get the comment from the visitor in this way, I simply DON'T KNOW to whom to answer.\r
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\n" ); document.write( "\n" ); document.write( "If you really want to get the response from me to your message/\"comment\",
\n" ); document.write( "then place the problem's ID number to your message/comment.\r
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\n" ); document.write( "\n" ); document.write( "It is the only way to support a two-sides/(two-ways) dialog.\r
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