If a polynomial graph touches the x-axis at one point and crosses it at another, the total number of real zeroes (counting the touch as repeated) is at least:

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Accepted Answer

3. A touch counts as a repeated zero (2 coincident) and a crossing is 1 more, so at least 3 zeroes, requiring degree at least 3.

If a polynomial graph touches the $x$ -axis at one point and crosses it at another, the total number of real zeroes (counting the touch as repeated) is at least:

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