The roots of a quadratic equation are \(\frac{-1}{2}\) and \(\frac{2}{3}\). Find the equation.
A
\(6x^2 - x + 2 = 0\)
B
\(6x^2 - x - 2 = 0\)
C
\(6x^2 + x - 2 = 0\)
D
\(6x^2 + x + 2 = 0\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
(x + \(\frac{1}{2}\)) (n - \(\frac{2}{3}\))
\(x^2 - \frac{2}{3^x} + \frac{x}{2} - \frac{1}{3}\)
\(6x^2 - 4n + 3n - 2 = 0\)
\(6x^2 - x - 2 = 0\)
Source: Myschool Past Questions Archive (Record #50122)