document.write( "Question 627997: Use the intermediate value theorem to show that the polynomial function has a zero given in the interval.\r
\n" ); document.write( "\n" ); document.write( "f(x)=3x^3+5x^2-6x+5;[-3,-1] \n" ); document.write( "
Algebra.Com's Answer #395387 by fcabanski(1391)\"\" \"About 
You can put this solution on YOUR website!
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( "3x^3+5x^2-6x+5 with x=-3 is 3*-27 + 5*9 + -6*-3 + 5 = -
\n" ); document.write( "3x^3+5x^2-6x+5 with x=-1 is -3 + 5 + 6 + 5 = +


\n" ); document.write( "Since one value is above y=0 and the other below y=0, the polynomial must have a zero within that interval.
\n" ); document.write( "

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( "

\n" );