document.write( "Question 358376: Using the intermediate value theorem, determine, if possible, whether the function f has a rea zero between a and b.\r
\n" ); document.write( "\n" ); document.write( "f(x)=x3+3x2-9x-13; a=1, b=2 \n" ); document.write( "

Algebra.Com's Answer #255763 by robertb(5830) $\"\"$ $\"About$

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Let $\"+1%3Cx%3C2\"$ . Then
\n" ); document.write( " $\"1%3Cx%5E3%3C8\"$ ,
\n" ); document.write( " $\"1%3Cx%5E2%3C4\"$ ,or $\"3%3C3x%5E2%3C12\"$ ,and
\n" ); document.write( " $\"-18%3C-9x%3C-9\"$ . Thus,after adding up all the corresponding sides,
\n" ); document.write( " $\"-14%3Cx%5E3%2B3x%5E2-9x%3C11\"$ .
\n" ); document.write( "This is the same as $\"-27%3Cx%5E3%2B3x%5E2-9x-13%3C-2\"$ , after subtracting 13 from all sides.
\n" ); document.write( "Since all values of the polynomial are negative, (between -2 and -27), then by the IVT, there cannot be a zero for f(x) between 1 and 2.\r
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