Explanation

For px² − 40x + 96 = 0 with roots α, β, we need α + β = 40/p and αβ = 96/p with α, β even integers. Trying p = 4 gives x² − 10x + 24 = 0 with roots 4 and 6, both even — this works. The values p = 1, 2, 3 give discriminants 1216, 208 and 448, none perfect squares, so the roots are not even integers. Hence p = 4, option D.