SOLUTION: Use the Intermediate Value Theorem and a graphing utility to find graphically any intervals of length 1 in which the polynomial function is guaranteed to have a zero, and (b) use t

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use the Intermediate Value Theorem and a graphing utility to find graphically any intervals of length 1 in which the polynomial function is guaranteed to have a zero, and (b) use t      Log On


   

Question 657769: Use the Intermediate Value Theorem and a graphing utility to find graphically any intervals of length 1 in which the polynomial function is guaranteed to have a zero, and (b) use the zero or root feature of the graphing utility to approximate the real zeros of the function. Verify your answers in part (a) by using the table feature of the graphing utility.
f(x) = 2x^4 + 7/2 x^3 - 2
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
As the problem states, you will need a graphing calculator (or program). Jujst enter the equation
y=2x%5E4%2B%287%2F2%29x%5E3-2
And try to determine the integers between which the graph crosses the x-axis (where the zeros are). If your calculator/program has a trace function, then that can be very helpful.

Here's what the graph looks like:
graph%28400%2C+400%2C+-5%2C+5%2C+-5%2C+5%2C+2x%5E4%2B%287%2F2%29x%5E3-2%29
See if you can figure out the integers between which the graph crosses the x-axis.