If α and β are the roots of the equation x 2 + α x + β = 0 such that α ≠ β , then the number of integral values of x satisfying x - β - α 1 is

Question

If α and β are the roots of the equation x 2 + α x + β = 0 such that α ≠ β , then the number of integral values of x satisfying x - β - α 1 is, 0, 1, 2, more than 2

MARKS App · Accepted Answer

α , β are roots of x 2 + α x + β = 0 ⇒ α + β = - α and α β = β ⇒ α = 1 , β = - 2 Now, x + 2 - 1 1 ⇒ - 1 x + 2 - 1 1 ⇒ 0 x + 2 2 ⇒ - 2 x + 2 2 , x + 2 ≠ 0 ⇒ - 4 x 0 , x ≠ - 2 ⇒ x ∈ - 4 , - 2 ∪ - 2,0 So, there are two integral values of x , i.e. - 3 , - 1

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