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Step 1 :

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Intermediate value theorem :

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Suppose that f is continuous on the closed interval $\"\"$ and let N be any number between $\"\"$ and $\"\"$ where $\"\"$ . Then there exists a number c in $\"\"$ such that $\"\"$ .

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Step 3 :

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The function is $\"\"$ and the point is $\"\"$ .

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The function is continuous for all values of x, except at $\"\"$

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Hence, The function $\"\"$ is continuous on the interval $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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It follows that $\"\"$ and $\"\"$ .

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Hence, the intermediate value theorem says there is a number c such that $\"\"$ .

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The function $\"\"$ has at least one root c in the interval $\"\"$ .

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Solution :

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The function $\"\"$ has at least one root c in the interval $\"\"$ .

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