The problem to use the intermediate value theorem to show that there is a root of the given equation in the specified interval.. sin(x)= x^2-x, (1,2). can someone see if this is correct? . f(x) = sin(x) - x^2 + x, then f is continuous since sin(x) and x^2 - x are continuous and their composition is also continuous. sin(x) = x^2 - x which is equivalent to showing that f(x) = 0. f(1) = 0.841 and f(2) = -1.091, 0 s lying between f(1) and f(2). since f is continuous, there is a c in (1,2) such that f(c) = 0. there is a root to the equation. sin(x) = x^2 - x.