If the roots of the equation x2+2ax+b=0 are real and distinct and they differ by at most 2m, then b lies in the interval

Let the roots be α,β.∴ α+β=−2a and αβ=bGiven, |α−β|≤2m or     |α−β|2≤(2m)2 or     (α+β)2−4ab≤4m2 or     4a2−4b≤4m2⇒    a2−m2≤b and discriminant D>0 or 4a2−4b>0⇒    a2−m2≤b and b