Question

Let S is the set of all integral values of X satisfying the both following two conditions a) (X²+5)|36 b) X≥3 then find the cardinality of S​

Answer 1

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Let S be the set of all non-zero real numbers α such that the quadratic equation αx

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 intervals is(are) subset(s) of S?

This question has multiple correct options

Medium

Solution

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Correct options are A) and D)

Given, quadratic equation αx

2

−x+α=0 has two distinct real roots x

1

and x

2

satisfying the inequality ∣x

1

−x

2

∣<1.

x

1

+x

2

=

α

1

and x

1

x

2

=1

∣x

1

−x

2

∣=∣

(x

1

+x

2

)

2

−4x

1

x

2

∣=∣

α

2

1

−4

∣<1

⇒0<

α

2

1

−4<1

⇒4<

α

2

1

<5

⇒α

2

>

5

1

and α

2

<

4

1

∴α∈(

2

−1

,

5

−1

)∪(

5

1

,

2

1

)