SOLUTION: Using the intermediate value theorem, determine, if possible, whether the function f has a rea zero between a and b. f(x)=x3+3x2-9x-13; a=1, b=2

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Using the intermediate value theorem, determine, if possible, whether the function f has a rea zero between a and b. f(x)=x3+3x2-9x-13; a=1, b=2      Log On


   

Question 358376: Using the intermediate value theorem, determine, if possible, whether the function f has a rea zero between a and b.
f(x)=x3+3x2-9x-13; a=1, b=2
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Let +1%3Cx%3C2. Then
1%3Cx%5E3%3C8,
1%3Cx%5E2%3C4,or 3%3C3x%5E2%3C12,and
-18%3C-9x%3C-9. Thus,after adding up all the corresponding sides,
-14%3Cx%5E3%2B3x%5E2-9x%3C11.
This is the same as -27%3Cx%5E3%2B3x%5E2-9x-13%3C-2, after subtracting 13 from all sides.
Since all values of the polynomial are negative, (between -2 and -27), then by the IVT, there cannot be a zero for f(x) between 1 and 2.