High resolution solution proves that the equation x ^ 3-4x ^ 2 + 1 = 0 has at least one real root between 1 and 4 This is a high number, problem-solving process

High resolution solution proves that the equation x ^ 3-4x ^ 2 + 1 = 0 has at least one real root between 1 and 4 This is a high number, problem-solving process

Let f (x) = x ^ 3-4x ^ 2 + 1
f(1)=-20
According to the intermediate value theorem, f (x) = x ^ 3-4x ^ 2 + 1 has at least one real root between 1 and 4