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: Option B
Explanation
((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 + 3sqrt{3} – 3sqrt{3} – 3) = 0)
(x^{2} – 3x – xsqrt{3} – 3x + xsqrt{3} + 6 = 0)
(x^{2} – 6x + 6 = 0)