As the quadratic equation is 2x^{2}-x+p = 0

For factors to be rational the discriminant of the equation must be a perfect square.

Discriminant = b^{2} - 4ac = 1 - 4 x 3 x p = 1 - 8p

**If 1 - 8p = (a)**^{2} where a is any integer then the quadratic equation will have linear factor.

Suppose, a = 7

1 - 8p = (7)^{2}

1 - 8p = 49

-8p = 48

p = -6