If the equation, x^2+ 2ax+b=0 and its roots
are real and distinct, and they differ by at most 2 m,
then where does b lies?
Answers
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Step-by-step explanation:
Let α, β be the roots of x
2
+2ax+b=0......(1)
⇒α+β=−2a and αβ=b
By hypothesis
∣α−β∣≤2m
⇒(α−β)
2
≤4m
2
⇒(α+β)
2
−4αβ≤4m
2
⇒4a
2
−4b≤4m
2
⇒a
2
−b≤m
2
......(2)
And discriminant of (1) is >0
⇒4a
2
−4b>0
⇒b<a
2
......(3)
From (2) and (3)
a
2
>b≥(a
2
−m
2
)
b∈[a
2
−m
2
,a
2
)
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