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|≤2mor  |α−β|2≤(2m)2or  (α+β)2−4ab≤4m2or  4a2−4b≤4m2⇒ a2−m2≤b and discriminant D>0 or 4a2−4b>0⇒ a2−m2≤b and b