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From the equation whose roots are x = \(\frac{1}{2}\) and -\(\frac{2}{3}\)

Mathematics
WAEC 2011

From the equation whose roots are x = \(\frac{1}{2}\) and -\(\frac{2}{3}\)
  • A. 6x2 - x + 2 = 0
  • B. 6x2 - x - 2 = 0
  • C. 6x2 + x + 2 = 0
  • D. 6x2 + x - 2 = 0
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Correct Answer: Option D
Explanation
x = \(\frac{1}{2}\) and x = \(\frac{-2}{3}\)

expand (x - \(\frac{1}{2}\))(x + \(\frac{2}{3}\)) = 0

x(x + \(\frac{2}{3}\)) - \(\frac{1}{2}(x + \frac{2}{3}\)) = 0

x2 + \(\frac{4x - 3x}{6} - \frac{2}{6} = 0\)

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

6x2 + x - 2 = 0

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