The number of all possible positive integral values of α for which the roots of the quadratic equation, 6x² - 1x + α = 0 are rational numbers is

6x² - 1x + α = 0
given roots are rational ⇒D must be the perfect square
⇒1² - 24α = λ²
⇒maximum value of α is 5
α = 1 ⇒ λ ∈ I
α = 2 ⇒ λ ∈ I
α = 3 ⇒ λ ∈ I
α = 4 ⇒ λ ∈ I
α = 5 ⇒ λ ∈ I
⇒3 integral value