Find the quadratic equation whose roots are \(\frac{2}{3}\) and - 1
A
3x\(^2\) - x - 2 = 0
B
3x\(^2\) + x + 2 = 0
C
3x\(^2\) + x - 2 = 0
D
3x\(^2\) + x - 1 = 0
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
The roots are \(\frac{2}{3}\) and - 1
Using x\(^2\) - (\alpha + \beta)x + \alpha\beta = 0
\alpha + \beta = \(\frac{2}{3}\) + (-1) = \(\frac{2}{3}\) - 1 = \(\frac{-1}{3}\)
\alpha\beta = \(\frac{2}{3}\) x (-1) = \(\frac{-2}{3}\)
x\(^2\) - (\(\frac{-1}{3}\) )x + (\(\frac{-2}{3}\)) = 0
multiply through by 3
3x\(^2\) + x - 2 = 0
Source: Myschool Past Questions Archive (Record #71787)