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

Step-by-step solution

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