Explanation

Put t = α/β. Since αβ = k/2 < 0, the roots have opposite signs, so t < 0. Now α/β + β/α = t + 1/t, and for t < 0 we have t + 1/t + 2 = (t+1)²/t ≤ 0, i.e. t + 1/t ≤ −2. Thus the expression never exceeds −2, and −2 is its maximum (least upper bound): option B. Option A (2) would apply if the roots had the same sign.