If the equation 2x² - 7x + 12 = 0 has two roots α and β, then the value of (α/β) + (β/α) is -

Solution:
Given Equation 2x² - 7x + 12 = 0
roots are α , β

We know,
∴ αβ = c/a
α + β = - b/a

∴ α + β = - (- 7/2) = 7/2
∴ αβ = 12/2 = 6

Now, α/β + β/α = (α² + β²)/αβ
= {(α + β)² - 2αβ}/αβ
= {(7/2)² - 2 . 6}/6
= {(49/4) - 12}/6
= {(49 - 48)/4}/6
= 1/24