If α and β are the roots of the equation 3x² + 5x – 2 = 0, find the value of 1/α + 1/β

Step 1: Recall Vieta’s formulas
For ax² + bx + c = 0:
Sum of roots: α + β = -b/a
Product of roots: αβ = c/a

Step 2: Find sum and product
Here: a = 3, b = 5, c = -2
α + β = -5/3
αβ = -2/3

Step 3: Express 1/α + 1/β
1/α + 1/β = (β + α)/(αβ)

Step 4: Substitute values
= (-5/3)/(-2/3)
= (-5/3) × (-3/2)
= 15/6
= 5/2