JEE Advanced2015MathematicsQuadratic EquationActual
Let S be the set of all non - zero real numbers α such that the quadratic equation α x 2 - x + α = 0 has two distinct real roots x 1 a n d x 2 satisfying the inequality x 1 - x 2 < 1 . Which of the following intervals is(are) a subset(s) of S?
Options
- A- 1 2 , - 1 5
- B- 1 5 , 0
- C0 , 1 5
- D1 5 , 1 2
Correct answer
A. - 1 2 , - 1 5
Step-by-step solution
α x 2 - x + α = 0 x 1 - x 2 < 0 1 - 4 α 2 α < 1 1 - 4 α 2 < | α | 1 - 4 α 2 < α 2 α 2 - 1 5 > 0 α ∈ - ∞ , - 1 5 ∪ 1 5 , ∞ Also, 1 - 4 α 2 > 0 α 2 - 1 4 < 0 α - 1 2 α + 1 2 < 0 α ∈ - 1 2 , 1 2 Taking intersection α ∈ - 1 2 , - 1 5 ∪ 1 5 , 1 2