The roots of a quadratic equation are \((3 - \sqrt{3})\) and \((3 + \sqrt{3})\). Find its equation.

A.

\(x^{2} - 6x - 9 = 0\)

B.

\(x^{2} - 6x + 6 = 0\)

C.

\(x^{2} + 6x - 9 = 0\)

D.

\(x^{2} + 6x + 6 = 0\)

Correct answer is B

\((x - \alpha)(x - \beta) = 0\)

\((x - (3 - \sqrt{3}))(x - (3 + \sqrt{3})) = 0\)

\((x^{2} - (3 - \sqrt{3})x - (3 + \sqrt{3})x + (9 + 3\sqrt{3} - 3\sqrt{3} - 3) = 0\)

\(x^{2} - 3x - x\sqrt{3} - 3x + x\sqrt{3} + 6 = 0\)

\(x^{2} - 6x + 6 = 0\)