Question

Help I will give a lot of points and stuff

Answer 1

• x² - 20x - 12 = 0

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