What ideas have you had so far?
Let p be a prime number and K an integer such that X^2 + kX + P = 0 has two positive interger solutions . What is the value of K+P?
If α and β are the roots of a quadratic equation ax^2 + bx + c = 0, then the sum of the roots = -b/a and the product of the roots = c/a.
In the given problem α + β = - k and αβ = p.
Since p is a prime, α = p and β = 1.
So α + β = - k = p + 1.
Hence k + p = -1.