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If a continuous function takes a positive value at one x and a negative value at another x, there is at least one zero between those two x-values. This is because the graph must cross the x-axis (where $y=0$) to move from above the axis to below it without breaking.

Conditions: The function is continuous on the interval between the two x-values.; One endpoint value is positive and the other is negative.

If a continuous function takes a positive value at one x and a negative value at another x, there is at least one zero between those two x-values. This is because the graph must cross the x-axis (where $y=0$) to move from above the axis to below it without breaking.

Conditions: The function is continuous on the interval between the two x-values.; One endpoint value is positive and the other is negative.