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Quadratic Equation and Inequalities question

2015 · Shift 2 · Q21

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JEE Advanced
Mathematics
Quadratic Equation and Inequalities
2015 · Shift 2 · Q21

Quadratic Equation and Inequalities question

2015 · Shift 2 · Q21

JEE AdvancedMathematicsQuadratic Equation and InequalitiesMultiple correct+4 / −1

Let

S

be the set of all non-zero real numbers

\alpha

such that the quadratic equation

\alpha {x^2} - x + \alpha = 0

has two distinct real roots

{x_1}

and

{x_2}

satisfying the inequality

\left| {{x_1} - {x_2}} \right| \lt 1.

Which of the following intervals is (are)

a

subset(s) os

S

?

A
$\left( { - {1 \over 2} - {1 \over {\sqrt 5 }}} \right)$
B
$\left( { - {1 \over {\sqrt 5 }},0} \right)$
C
$\left( {0,{1 \over {\sqrt 5 }}} \right)$
D
$\left( {{1 \over {\sqrt 5 }},{1 \over 2}} \right)$

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