Answer:
Step-by-step explanation:
Since [tex]f(x)=x^4-2x^2-1[/tex] yields a smooth continuous curve (there's no x value where f(x) is undefined). We can apply intermediate value theorem here.
Substitute 0 for x and f(0) = 0 - 2*0 - 1 = -1 < 0
Substitute 2 for 2 and [tex]f(2) = 2^4 - 2*2^2 - 1 = 16 - 8 - 1 = 7 > 0[/tex]
Since f(0) < 0 and f(2) > 0, by the intermediate value theorem, there's must be a point between 0 and 2 where the curve crosses the x axis (y = 0). Therefore this function is guaranteed to have a zero