document.write( "Question 935701: Use the intermediate value theorem to determine whether the polynomial function has a zero in the given interval f(x)=-2x^4+2x^2+4; [-2,-1] \n" ); document.write( "

Algebra.Com's Answer #568992 by josgarithmetic(39617) $\"\"$ $\"About$

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The square parentheses mean you can INCLUDE the boundaries of the interval.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "x=-2:
\n" ); document.write( " $\"-2%28x%5E4-x%5E2-2%29\"$
\n" ); document.write( " $\"-2%28%28-2%29%5E4-%28-2%29%5E2-2%29\"$
\n" ); document.write( " $\"-2%2816-4-2%29\"$
\n" ); document.write( " $\"%28neg%29%28pos%29\"$
\n" ); document.write( "NEGATIVE\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "x=-1:
\n" ); document.write( " $\"-2%28%28-1%29%5E4-%28-1%29%5E2-2%29\"$
\n" ); document.write( " $\"-2%281-1-2%29\"$
\n" ); document.write( " $\"-2%28-2%29\"$
\n" ); document.write( " $\"neg%2Aneg\"$
\n" ); document.write( "POSITIVE\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Polynomial functions are continuous everywhere. The function changes signs inside the given interval, so f must cross the x-axis, and therefore has a zero in the interval. \n" ); document.write( "

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