Quadratic EquationHard
Question
The value of α for which the sum of the squares of the roots of the equation x2 - (a - 2)x - a - 1 = 0 assume the least value is
Options
A.1
B.0
C.3
D.2
Solution
x2 - (a - 2)x - a - 1 = 0
⇒ α + β = a - 2
αβ = - (a + 1)
α2 + β2 = (α + β)2 - 2αβ
a2 - 2a + 6 = (a - 1)2 + 5
⇒ a = 1.
⇒ α + β = a - 2
αβ = - (a + 1)
α2 + β2 = (α + β)2 - 2αβ
a2 - 2a + 6 = (a - 1)2 + 5
⇒ a = 1.
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