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

Question 627996: Use the intermediate value theorem to show that the polynomial function has a zero in the given interval.
f(x)=7x^4-2x^2+4x-1;[-3,0]
f(-3)=?
Answer by fcabanski(1391) (Show Source): 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.

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.

7x^4-2x^2+4x-1 for x=0 is -1
7x^4-2x^2+4x-1 for x=-3 is 7*81 -18 -12 -1 = +

This polynomial has a zero in the given interval.

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.)

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