Reason : For quadratic equation : x2+bx+72=0 α+β=72 [using product of roots] Now, for α×β=72, possible positive values are α=1‌&‌β=72⇒b=–73 α=2‌&‌β=36⇒b=–38 α=3‌&‌β=24⇒b=–27 α=4‌&‌β=18⇒b=–22 α=6‌&‌β=12⇒b=–18 α=8‌&‌β=9⇒b=–17 {using sum of roots) Nor for αβ= 72, possible negative values are α=–1‌&‌β=–72⇒b=73 α=–2‌&‌β=–36⇒b=38 α=–3‌&‌β=–24⇒b=27 α=–4‌&‌β=–18⇒b=22 α=–6‌&‌β=–12⇒b=18 α=–8‌&‌β=–9⇒b=17 hence total number of possible value of b are 12. Hence option (1) is correct.