Find the equation whose roots are \(\frac{2}{3}and \frac{-1}{4}\)
MATHEMATICS
WAEC 1998
Find the equation whose roots are \(\frac{2}{3}and \frac{-1}{4}\)
- A. \(12x^2-5x-2=0\)
- B. \(12x^2-11x+2=0\)
- C. \(x^2-\frac{11}{12}x+2=0\)
- D. \(x^2+\frac{11}{12}x-2=0\)
Correct Answer: A. \(12x^2-5x-2=0\)
Explanation
x\(^2\) - (sum of given roots)x + (product of given roots ) = 0
x\(^2\) - (\(\frac{2}{3} + \frac{-1}{4}\))x + (\(\frac{2}{3} * \frac{-1}{4}\)) = 0
x\(^2\) - (\(\frac{8 - 3}{12}\))x + (\(\frac{- 2}{12}\))
x\(^2\) - \(\frac{5}{12}\)x + \(\frac{- 2}{12}\)
multiply through by the LCM 12
12 * x\(^2\) - 12 * \(\frac{5}{12}\)x + 12 * \(\frac{- 2}{12}\)
12x\(^2\) - 5x - 2 = 0
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