Find the equation whose roots are (frac{2}{3}and frac{-1}{4})

Find the equation whose roots are \(\frac{2}{3}and \frac{-1}{4}\)

\(12x^2-5x+2=0\)
\(12x^2-11x+2=0\)
\(x^2-\frac{11}{12}x+2=0\)
\(x^2+\frac{11}{12}x-2=0\)
\(12x^2+11x+2=0\)

The correct answer is: A

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