Question

Anonymous a year ago

Answer 1

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.