Answer :
Final answer:
The splitting field of x⁴ - 10x² + 21 over Q is Q(√3, √7).
Explanation:
Splitting Fields of x⁴ - 10x² + 21 over Q
To find the splitting field of a polynomial, we need to find the field extension over which the polynomial completely factors into linear factors. The polynomial x⁴ - 10x² + 21 can be factored as (x² - 7)(x² - 3), where each factor is irreducible over Q. Since Q is a field, the splitting field for x⁴ - 10x² + 21 over Q is the smallest field extension of Q that contains the roots of the irreducible factors, which in this case is Q(√3, √7).
