Use the Intermediate Value Theorem to determine whether there is a zero of the given function f in the indicated intervals

Question

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

Answer 1

The IVT states that if a function is continuous (meaning it doesn't have any breaks, and all polynomials are) then if the value of the function at two different x values switches from positive to negative, or vice versa, then somewhere between those two is a zero. So plug in the endpoints for each interval and see if the values you get out switch signs. If so, then yes. i.e f(0) = 15 and f(1) = -3, therefore there is a zero between 0 and 1