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Can a fourth degree polynomial touch the x axis three times? - Answers

No, a fourth degree polynomial cannot touch the x-axis three times. A polynomial can touch the x-axis at an even number of points, which corresponds to the multiplicity of its roots. If it touches the x-axis at three points, one of those points would have to be of odd multiplicity, which would make the total multiplicity odd, contradicting the fact that a fourth degree polynomial has an even degree. Thus, it can touch the x-axis at either 0, 2, or 4 points.



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Can a fourth degree polynomial touch the x axis three times? - Answers

https://math.answers.com/math-and-arithmetic/Can_a_fourth_degree_polynomial_touch_the_x_axis_three_times

No, a fourth degree polynomial cannot touch the x-axis three times. A polynomial can touch the x-axis at an even number of points, which corresponds to the multiplicity of its roots. If it touches the x-axis at three points, one of those points would have to be of odd multiplicity, which would make the total multiplicity odd, contradicting the fact that a fourth degree polynomial has an even degree. Thus, it can touch the x-axis at either 0, 2, or 4 points.



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https://math.answers.com/math-and-arithmetic/Can_a_fourth_degree_polynomial_touch_the_x_axis_three_times

Can a fourth degree polynomial touch the x axis three times? - Answers

No, a fourth degree polynomial cannot touch the x-axis three times. A polynomial can touch the x-axis at an even number of points, which corresponds to the multiplicity of its roots. If it touches the x-axis at three points, one of those points would have to be of odd multiplicity, which would make the total multiplicity odd, contradicting the fact that a fourth degree polynomial has an even degree. Thus, it can touch the x-axis at either 0, 2, or 4 points.

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      No, a fourth degree polynomial cannot touch the x-axis three times. A polynomial can touch the x-axis at an even number of points, which corresponds to the multiplicity of its roots. If it touches the x-axis at three points, one of those points would have to be of odd multiplicity, which would make the total multiplicity odd, contradicting the fact that a fourth degree polynomial has an even degree. Thus, it can touch the x-axis at either 0, 2, or 4 points.

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