‌=−a±√a2−b let, α‌=−a+√a2−b β‌=−a−√a2−b so, |α−β|=2√a2−b given that 2√a2−b≤2m ‌⇒‌‌a2−b≤m2 ‌⇒‌‌b≥a2−m2 Also, for real and distinct roots D=4a2−4b>0 ⇒‌‌b<a2 Hence, a2−m2≤b ⇒‌‌b∈[a2−m2,a2)
