$\"\"$

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Intermediate value theorem :

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Let $\"\"$ denote a polynomial function.If $\"\"$ and if $\"\"$ and $\"\"$ are of opposite sign, there is at least one real zero of $\"\"$ between $\"\"$ and $\"\"$ .

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$\"\"$

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The polynomial function is $\"\"$ and the interval is $\"\"$ .

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Evaluate $\"\"$ at $\"\"$ and $\"\"$ .

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Consider $\"\"$ .

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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 at least one real zero of $\"\"$ in the interval $\"\"$ .

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$\"\"$

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$\"\"$ and $\"\"$ .