Question

X1
X2 satisfying the inequality
A Let S be the set of all non-zero real numbers a such
that the quadratic equation. ax2 - x + a = 0 has two
distinct real roots
and
n-12|< 1. Which of the following intervals is
(are) a subset(s) of S?
[2015]
1 1
2: 5
(b)
(a)
0 (0:1) (a) (153)​

Answer 1

Answer:

PLEASE DO CORRECT YOUR QUESTIONS

Answer 2

Answer:

Step-by-step explanation:

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

​

)