How to find the X-intercept of x^3-3x+1

Question

How do I go about finding the x-intercept of the function:

h(x)=x^3-3x+1

Answer 1

Plot it on Desmos ? As it’s a polynomial it is continuous and differentiable everywhere, so you can use the intermediate value theorem to narrow down possible intervals. For example h(2) > 0 and h(1) < 0 so there must be at least one zero in the interval (1,2) . Compare h(1) to h(1.5) etc to narrow down the interval. You might as well use technology eg Desmos for this