NTSE Stage 2 SAT 2017 Question Paper

Reason :
Let roots of quadratic equation :
x2–‌bx+6=0‌are‌α‌&‌γ.
and roots of quadratic equation :
x2–‌bx+c=0‌are‌α‌&‌β
Then : we have

β

γ

=

3

4

...(2)
Also from (1) we get

αβ

αγ

=

6

c

⇒

β

γ

=

6

c

...(3)
from (2) & (3) we get

3

4

=

6

c

⇒c=8
Now using c = 8, second quadratic equation
x2−6x+c=0 become
x2−6x+8=0
on solving x2−6x+8=0,we get x=2 & 4.
If common root is 2 then by putting x = 2 in equation
x2−bx+6=0 we get
(2)2−b×4+6=0⇒ b=5
If common root is 4 then by putting x = 4 in equation
x2−bx+6=0 we get
(4)2−b×4+6=0 ⇒ b=

11

2

But sum of roots α+β=5‌&‌α×β=6 is possible only if common root is 2.
Hence option (2) is correct.