SOLUTION: Use the intermediate value theorem to show that the polynomial function has a zero given in the interval. f(x)=3x^3+5x^2-6x+5;[-3,-1]

Algebra ->  Test -> SOLUTION: Use the intermediate value theorem to show that the polynomial function has a zero given in the interval. f(x)=3x^3+5x^2-6x+5;[-3,-1]      Log On


   

Question 627997: Use the intermediate value theorem to show that the polynomial function has a zero given in the interval.
f(x)=3x^3+5x^2-6x+5;[-3,-1]
Answer by fcabanski(1391) About Me  (Show Source):
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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.


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.


3x^3+5x^2-6x+5 with x=-3 is 3*-27 + 5*9 + -6*-3 + 5 = -
3x^3+5x^2-6x+5 with x=-1 is -3 + 5 + 6 + 5 = +


Since one value is above y=0 and the other below y=0, the polynomial must have a zero within that interval.

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