SOLUTION: Using the intermediate value theorem, determine whether the function has at least one real zero between a and b. a. f(x) = x 3 + 3x 2 – 9x – 13 a = - 5 b = - 4

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Using the intermediate value theorem, determine whether the function has at least one real zero between a and b. a. f(x) = x 3 + 3x 2 – 9x – 13 a = - 5 b = - 4       Log On


   

Question 907423: Using the intermediate value theorem, determine whether the function has at least one real zero between a and b.
a. f(x) = x 3 + 3x 2 – 9x – 13 a = - 5 b = - 4




b. f(x) = 3x 2 – 2x – 11 a = - 3 b = - 2
Thank you for the help in advance
Found 2 solutions by ewatrrr, solver91311:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x^3 + 3x^2 – 9x – 13 |Note use of ^ (uppercase 6)
f(-5) = -18
f(-4) = 7
Negative to positive
Obviously curve crosses x-axis (has at least one real zero ) between -5 and -4.
Graphing Calculator a must
If not...
dl the FREE graph software at
http://www.padowan.dk.com

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Both problems are done the same way. Calculate and . If the sign of is different than the sign of , then for a function that is continuous over the given interval, there is at least one real zero in the interval. If the signs are the same, the existence of a zero cannot be guaranteed, nor can the possibility be eliminated. Both of your problems are polynomial functions so there are no continuity issues.

John

My calculator said it, I believe it, that settles it