amirahbarker
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anonymous a year ago
1.Ray and Kelsey are working to graph a third-degree polynomial function that represents the first pattern in the coaster plan. Ray says the third-degree polynomial has 4 intercepts. Kelsey argues the function can have as many as 3 zeros only. Is there a way for the both of them to be correct? Explain your answer

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Aliwohaish12
Of course there is no way for them to be both correct, since they contradict each other. Here is how to prove Ray incorrect. Suppose that a polynomial has four roots: s, t, u, and v. If the polynomial were evaluated at any of these values, it would have to be zero. Therefore, the polynomial can be written in this form. p(x)(x - s)(x - t)(x - u)(x - v), where p(x) is some non-zero polynomial This polynomial has a degree of at least 4. It therefore cannot be cubic. Now prove Kelsey correct. We have already proved that there can be no more than three roots. To prove that a cubic polynomial with three roots is possible, all we have to do is offer a single example of that. This one will do. (x - 1)(x - 2)(x - 3) This is a cubic polynomial with three roots, and four or more roots are not possible for a cubic polynomial. Kelsey is correct. Incidentally, if this is a roller coaster we are discussing, then a cubic polynomial is not such a good idea, either for a vertical curve or a horizontal curve.

Ray is incorrect and Kelsey is correct.

What is third degree polynomial?

Third-degree polynomial is of the form [tex]p(x) = ax^{3} +b x^{2} +cx +d[/tex]where 'a' is not equal to zero. It is also called cubic polynomial as it has degree 3.

What is intercept?

The intercepts are the points where a graph crosses the x and y axes.

They contradicting  each other.

Ray incorrect.

Suppose that a polynomial has four roots: s, t, u, and v. If the        polynomial were evaluated at any of these values, it would have to be zero. Therefore, the polynomial can be written in this form. p(x)(x - s)(x - t)(x - u)(x - v), where p(x) is some non-zero polynomial .

This polynomial has a degree of at least 4. It therefore cannot be cubic.

Kelsey correct  because

We have already proved that there can be no more than three roots. To prove that a cubic polynomial with three roots is possible all we have to do is offer a single example of that. This one will do. (x - 1)(x - 2)(x - 3) This  is a cubic polynomial with three roots, and four or more roots are not possible for a cubic polynomial. Kelsey is correct.

Learn more about intercept and three degree polynomial here:

https://brainly.com/question/14180189

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