NIMCET 2011 Question Paper with solutions

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Question : 26 of 120

Marks: +1, -0

The least integral value of k for which

(k-2) x^{2}+8 x+k+4>0

for all

x \in R

, is

5
4
3
6

Solution:

Given,

(k-2) x^{2}+8 x+k+4>0

(k-Z)>0

and

D<0

⇒ k>2

and

D<0

......(i)
Now,

64-4(k-2)(k+4)<0

⇒ 16-(k^{2}+2 k-8)<0

⇒ k^{2}+2 k-8>16

⇒ k^{2}+2 k-24>0

⇒ (k+6)(k-4)>0

⇒ k<-6

or

k>4

....(ii)

∴

From Eqs. (i) and (ii), we get

k>4

∴

Hence, least integral value of

k

is

5 .

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