The roots of a quadratic equation are \((3 - \sqrt{3})\) and \((3 + \sqrt{3})\). Find
FURTHER MATHEMATICS
WAEC 2010
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: B. \(x^{2} - 6x + 6 = 0\)
Explanation
\((x - \alpha)(x - \beta) = 0\)
\((x - (3 - \sqrt{3}))(x - (3 + \sqrt{3})) = 0\)
\((x^{2} - (3 - \sqrt{3})x - (3 + \sqrt{3})x + (9 + 3\sqrt{3} - 3\sqrt{3} - 3) = 0\)
\(x^{2} - 3x - x\sqrt{3} - 3x + x\sqrt{3} + 6 = 0\)
\(x^{2} - 6x + 6 = 0\)
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