Consider the following equation. 3x4 − 8x3 + 3 = 0, [2, 3] (a) explain how we know that the given equation must have a root in the given interval. let f(x) = 3x4 − 8x3 + 3. the polynomial f is continuous on [2, 3], f(2) = < 0, and f(3) = > 0, so by the intermediate value theorem, there is a number c in (2, 3) such that f(c) = . in other words, the equation 3x4 − 8x3 + 3 = 0 has a root in [2, 3]. (b) use newton's method to approximate the root correct to six decimal places.