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transgalactic
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i added my question and how i thought to solve it in the
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A minimal polynomial is a polynomial of the least degree that has a given root. It is the smallest polynomial that has the given root as a solution.
To find the minimal polynomial of a given root, you can use the method of substitution. Plug in the root value into the polynomial and see if it equals to zero. If it does, then that polynomial is the minimal polynomial of the root.
Yes, a minimal polynomial can have multiple roots. This means that the polynomial has more than one solution that makes it equal to zero. This can occur when the root has a multiplicity greater than one.
The degree of a minimal polynomial is determined by the degree of the given root. If the root has a degree of n, then the minimal polynomial will have a degree of n.
The minimal polynomial is significant in many areas of mathematics, including linear algebra and number theory. It helps us understand the relationship between a root and its corresponding polynomial and can be used to solve various problems and equations.