Use the Intermediate Value Theorm to find if there is a 0 of the given function in the indicated interval.?

Question

function: f(x)=8x^4 - 23x^3 + 23x^2 - 26x + 15
Intervals: [-1,0], [0,1], [1,2], [2,3]

For some reason, my instructor didn't cover how to do these in class, but he assigned them for our homework. I have no idea how to go about doing them. Any help is appreciated, thanks!

Answer 1

The function is polynomial, so it's surely continuous. Then you can use the Intermediate Value Theorem. You have just to calculate f(x) in the limits of the intervals. If 0 is between these two values, then it exists in the interval.

I make just the first, leaving you the others!!!

f(-1)=8+23+23+26+15=95
f(0)=15

In the first interval there're no 0s.

Answer 2

Evaluate the function at the endpoints of each interval. If if one of them is positive and the other is negative then there must be a zero somewhere in between. This is because the function is continuous. The only way to get to a positive number from a negative number (or vice versa) is by going past zero.