document.write( "Question 627996: Use the intermediate value theorem to show that the polynomial function has a zero in the given interval.
\n" ); document.write( "f(x)=7x^4-2x^2+4x-1;[-3,0]\r
\n" ); document.write( "\n" ); document.write( "f(-3)=? \n" ); document.write( "

Algebra.Com's Answer #395388 by fcabanski(1391) $\"\"$ $\"About$

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The intermediate value theorem is basically this: If a point on a continuous curve has a point above a line, and it has a point below a line, then it must have a point on the line. This means that if there's a polynomial with a value above y=0 and below y=0 then it must have a zero in that interval.

\n" ); document.write( "The bottom line is: when given an interval and a polynomial check the low value and high value. If one is positive and the other negative then there must be a zero within that interval.

\n" ); document.write( "7x^4-2x^2+4x-1 for x=0 is -1
\n" ); document.write( "7x^4-2x^2+4x-1 for x=-3 is 7*81 -18 -12 -1 = +

\n" ); document.write( "This polynomial has a zero in the given interval.
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Hope the solution helped. Sometimes you need more than a solution. Contact fcabanski@hotmail.com for online, private tutoring, or personalized problem solving (quick for groups of problems.) \n" ); document.write( "

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