A) \[{{\alpha }^{2}}+3\alpha -4=0\]
B) \[{{\alpha }^{2}}-5\alpha +4=0\]
C) \[{{\alpha }^{2}}-7\alpha +6=0\]
D) \[{{\alpha }^{2}}+5\alpha -6=0\]
Correct Answer: A
Solution :
\[\frac{x-5}{{{x}^{2}}+5x-14}>0\Rightarrow {{x}^{2}}+5x-14<x-5\] \[\Rightarrow {{x}^{2}}+4x-9<0\] \[\Rightarrow \]\[\alpha =-5,-4,-3,-2,-1,0,1\] \[\alpha =-5\]does not satisfy any of the options \[\alpha =-4\]satisfy the option \[{{\alpha }^{2}}+3\alpha -4=0\]
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