A) \[{{x}^{2}}+2\sqrt{2}x+1\]
B) \[{{x}^{2}}-2\sqrt{2}x+1\]
C) \[{{x}^{2}}+2\sqrt{2}x-1\]
D) \[{{x}^{2}}-2\sqrt{2}x-1\]
Correct Answer: B
Solution :
| Sum of roots \[=\left( \sqrt{2}+1 \right)+\sqrt{2}-1=2\sqrt{2}\] |
| Product of roots \[=\left( \sqrt{2}+1 \right)\left( \sqrt{2}-1 \right)=2-1=1\] |
| \[\therefore\] Polynomial is \[{{x}^{2}}-\] (sum of roots) x + product of roots \[{{x}^{2}}-2\sqrt{2}x+1\] |
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