NTSE Stage 2 SAT 2017 Question Paper

© examsiri.com

Question : 57 of 100

Marks: +1, -0

The value(s) of k for which

\x^2+5\k\x+\k^2+5

is exactly divisible by

\x+2

but not by

\x+ 3

is (are)

1
5
1,9
9

Solution:

Here,

\P(\x)=\x^2+5\K\x+\K^2 \and \P(-2) \P(-3)≠0

∴

4-10\K+\K^2+5=0

⇒

\K^2-10\K+9=0

⇒

(\K-9)(\K-1)=0

⇒

\K=1,9

.....(1)
Also

\P(-3)≠0

⇒

9-15\K+\K^2+5≠0

⇒

\K^2-15\K+14≠0

⇒

(\K-14)(\K-1)≠0

⇒

\K≠14,1\;\;\;\;\;\.....(2)

From (1) and (2) K = 9
Option (4) is correct.

© examsiri.com

Go to Question:

Prev Question

Next Question