If \alpha and \beta are the roots of the equation 3x\(^2\) + 5x - 2 = 0, find the value of 1/\alpha + 1/\beta
A
-5/3
B
-2/3
C
1/2
D
5/2
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
1/\alpha + 1/\beta = \beta+\alpha/\alpha\beta
3x\(^2\) + 5x - 2 = 0
x\(^2\) + 5x/3 - 2/3 = 0
\alpha\beta = -2/3
\beta+\alpha = -5/3
Thus; \beta+\alpha/\alpha\beta = -5/3 \div -2/3 = 5/2
Source: Myschool Past Questions Archive (Record #787)