SOLUTION: Use the intermediate value theorem for polynomials ot shoe that each polynomial function has a real zero between the numbers given. {{{f(x)=2x^3-9x^2+x+20}}}; 2 and 2.5

Question 44916: Use the intermediate value theorem for polynomials ot shoe that each polynomial function has a real zero between the numbers given.
; 2 and 2.5
Answer by Chris435435(8) (Show Source): You can put this solution on YOUR website!
Polynomials have the special property of being continuous. This means that you can draw the whole curve without ever lifting your pencil. Now all the Intermediate Value Theorem says is that since the polynomial is continous, then a real zero must exist between two values where one is positive and the other is negative. How do you go from a positive to a negative or vice versa? You must cross the x-axis and all the zeroes of a polynomial lie on the x-axis.
So if a real zero exists between 2 and 2.5, then we can be certain that for f(2) and f(2.5), one is positive and the other is negative. If these conditions hold, then there is a zero between 2 and 2.5.

Since f(2) is positive while f(2.5) is negative, a real zero exists between 2 and 2.5.
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