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Question

Number of integral values of k for which the equation (k2)x2+8x+k+4=0 has both roots real, distinct and negative is

A
0
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B
1
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C
2
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D
3
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Solution

The correct option is C 2
(K2)x2+8x+K+4=0
roots are real distinct and negative
D0, b2a< and af(0)>0
D=824(K2)(K+4)
=4(16K22K+4K8)
=4(16K22K+8)
=4(242KK2)0
K2+2K240
(12+6)(K4)0
K[6, 4](1)
b2a=82(K2)<0
1K2>0 K>2(2)
af(0)=(K2)(K+4)>
(, 4)(2, )(3)
From (1), (2) and (3)
K(2, 4)
K=3, 4 are integer.


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