SOLUTION: Please assist me with the following problem: Using the intermediate value theorem, determine, if possible, whether the function f has a real zero between a and b f(x)=3x^2-2x

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please assist me with the following problem: Using the intermediate value theorem, determine, if possible, whether the function f has a real zero between a and b f(x)=3x^2-2x      Log On


   

Question 165212: Please assist me with the following problem:
Using the intermediate value theorem, determine, if possible, whether the function f has a real zero between a and b
f(x)=3x^2-2x-11; a=2, b=3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's evaluate the left endpoint a=2


f%28x%29=3x%5E2-2x-11 Start with the given equation.


f%282%29=3%282%29%5E2-2%282%29-11 Plug in x=2.


f%282%29=3%284%29-2%282%29-11 Square 2 to get 4.


f%282%29=12-2%282%29-11 Multiply 3 and 4 to get 12.


f%282%29=12-4-11 Multiply -2 and 2 to get -4.


f%282%29=-3 Combine like terms.


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Let's evaluate the right endpoint b=3


f%28x%29=3x%5E2-2x-11 Start with the given equation.


f%283%29=3%283%29%5E2-2%283%29-11 Plug in x=3.


f%283%29=3%289%29-2%283%29-11 Square 3 to get 9.


f%283%29=27-2%283%29-11 Multiply 3 and 9 to get 27.


f%283%29=27-6-11 Multiply -2 and 3 to get -6.


f%283%29=10 Combine like terms.


So as x changes from 2 to 3, f(x) (ie y) changes from -3 to 10 which means that the graph MUST have crossed over the x-axis somewhere in between x=2 and x=3. So this shows that there is a zero between a and b