If ( \alpha, \beta ) are the roots of the equation ( x^2 + px + 12 = 0 ) and ( \alpha - \beta = 1 ) then the value of p is

For the quadratic equation x² + px + 12 = 0 with roots α and β, we have α + β = -p and αβ = 12. Given α - β = 1, squaring gives (α - β)² = 1, so α² - 2αβ + β² = 1. This means (α + β)² - 4αβ = 1. Substituting: p² - 4(12) = 1, giving p² - 48 = 1, so p² = 49 and p = ±7. Option C is correct. Using Vieta's formulas and the given difference of roots leads to the solution.