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 $x_{1}$ and $x_{2}$ satisfying the inequality $| x_{1} - x_{2} | < 1$ . Which of the following interval(s) is/are a subset of S?

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For a non-zero vector ¯a, the set of real numbers satisfying the inequality |(6−x)¯a|<|4¯a| consists of all x such that

The correct option is A 2<x<10Since ¯a is a non zero vector, we can divide both sides by it.We thus get |6−x|<4⇒6−x<4 and 6−x>−4⇒x>2 and x<10⇒x∈(2,10)

For a non-zero vector $¯ a$ , the set of real numbers satisfying the inequality $| (6 - x) ¯ a | < | 4 ¯ a |$ consists of all x such that

The correct option is A $2 < x < 10$
Since $¯ a$ is a non zero vector, we can divide both sides by it.
We thus get $| 6 - x | < 4$
$\Rightarrow 6 - x < 4$ and $6 - x > - 4$
$\Rightarrow x > 2$ and $x < 10$
$\Rightarrow x \in (2, 10)$