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?

Question

Let S be the set of all non - zero real numbers &#945; such that the quadratic equation &#945; x 2 - x + &#945; = 0 has two distinct real roots x 1 &#160; a n d &#160; x 2 satisfying the inequality x 1 - x 2 &#60; 1 . Which of the following intervals is(are) a subset(s) of S?

Aicharya · Accepted Answer

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

Let S be the set of all non - zero real numbers α such that the quadratic equation α x 2 - x +…

Solution

Let S be the set of all non - zero real numbers &#945; such that the quadratic equation &#945; x 2 - x +…

Solution

Let S be the set of all non - zero real numbers α such that the quadratic equation α x 2 - x +…