Answer:
Step-by-step explanation:
One root is given, 10 - 4√7.
Since the polynomial has to have rational roots and of a minimal degree, the other root is the conjugate of the given and the polynomial is of degree 2 minimum.
The polynomial is:
- (x - 10 - 4√7)(x - 10 + 4√7) = 0
- x² - (10 - 4√7 + 10 + 4√7)x + (10² - (4√7)²) = 0
- x² - 20x + 100 - 112 = 0
- x² - 20x - 12 = 0
