Quadratic EquationHard
Question
If the difference between the roots of the equation x2 + ax + 1 = 0 is less than √5, then the set of possible values of a is
Options
A.(-3, 3)
B.(-3, ∞)
C.(3, ∞)
D.(-∞, -3)
Solution
x2 + ax + 1 = 0
α + β = - a αβ = 1
|α - β| =
|α - β| =
a2 - 4 < 5
a2 - 9 < 0
a ∈ (-3, 3).
α + β = - a αβ = 1
|α - β| =
|α - β| =
a2 - 4 < 5
a2 - 9 < 0
a ∈ (-3, 3).
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