document.write( "Question 763973: On which interval does the Intermediate Value Theorem guarantee that the polynomial function f(x) = x4 + 7x2 − 9x − 1
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Algebra.Com's Answer #465157 by Edwin McCravy(20056)\"\" \"About 
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document.write( "A polynomial f(x) has a root on the interval [a,b] if f(a) and f(b)\r\n" );
document.write( "have different signs.\r\n" );
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document.write( "f(x) = x4 + 7x2 − 9x − 1\r\n" );
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document.write( "has a root on the interval [1,2] because the value at the left endpoint\r\n" );
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document.write( "f(1) = (1)4 + 7(1)2 − 9(1) − 1 = 1+7(1)-9-1 = -2\r\n" );
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document.write( "is negative and the value at the right endpoint\r\n" );
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document.write( "f(2) = (2)4 + 7(2)2 − 9(2) − 1 = 16+7(4)-18-1 = 25\r\n" );
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document.write( "is positive.  \r\n" );
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document.write( "It also has a root on the interval [-1,0] because the value at the left endpoint\r\n" );
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document.write( "f(-1) = (-1)4 + 7(-1)2 − 9(-1) − 1 = 1+7(1)+9-1 = 16\r\n" );
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document.write( "is positive and the value at the right endpoint\r\n" );
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document.write( "f(0) = (0)4 + 7(0)2 − 9(0) − 1 = 0+7(0)+0-1 = -1\r\n" );
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document.write( "is negative.\r\n" );
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document.write( "Edwin
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