Pierce Evans
10/10/2024 · Junior High School
3. Show that the equation \( x^{4}+4 x-1=0 \) has at least one root in the interval \( (-1,2) \).
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Using the Intermediate Value Theorem, we evaluate \( f(-1) = -4 \) and \( f(2) = 23 \). Since \( f(x) \) changes sign from negative to positive over the interval \( (-1, 2) \), there exists at least one root in this interval.
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