EXAMPLE 10 Show that there is a root of the equation 2x3 − 4x2 + 3x − 2 = 0 between 1 and 2. SOLUTION Let f(x) = 2x3 − 4x2 + 3x − 2 = 0. We are looking for a solution of the given equation, that is, a number c between 1 and 2 such that f(c) = . Therefore we take a = , b = , and N = in the Intermediate Value Theorem. We have

Step-by-step explanation:

First, it is needed to determined the values for x = 1 and x = 2:

The sign change within the interval is the most sound evidence of the root existence. According to the Intermediate Value Theorem, there is a number such that . Another finding is that is closer to 1 than to 2.

step-by-step explanation:

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