A) \[{{x}^{2}}+4x-1=0\]
B) \[{{x}^{2}}+4x+1=0\]
C) \[{{x}^{2}}-4x-1=0\]
D) \[\sqrt{2}{{x}^{2}}-4x+1=0\]
Correct Answer: A
Solution :
Let \[\alpha =\frac{1}{2+\sqrt{5}}\]and \[\beta =\frac{1}{2-\sqrt{5}}\] Sum of roots \[\alpha +\beta =-4\]and product of roots \[\alpha \beta =-1\] Thus required equation is \[{{x}^{2}}+4x-1=0\]
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