A) \[+\sqrt{3}\]
B) \[\sqrt{3}\,i\]
C) \[-\,\,\sqrt{3}\,\,\,i\]
D) \[-\,\,\sqrt{3}\,\,\,\]
Correct Answer: D
Solution :
\[{{x}^{2}}-\sqrt{3}=0\] \[\Rightarrow {{x}^{2}}-{{(3)}^{\frac{1}{2}}}=0\] \[\Rightarrow {{x}^{2}}-{{\left( {{3}^{\frac{1}{4}}} \right)}^{2}}=0\] \[\Rightarrow \left( x+{{3}^{\frac{1}{4}}} \right)\left( x-{{3}^{\frac{1}{4}}} \right)=0\] \[\therefore x={{3}^{\frac{1}{4}}}\,\,\]or \[=-{{3}^{\frac{1}{4}}}\] \[\therefore \] Product of roots \[={{3}^{\frac{1}{4}}}\times -{{3}^{\frac{1}{4}}}=-\sqrt{3}\] Note: Product of the roots of \[a{{x}^{2}}+bx+c=0\] is \[\frac{c}{a}\] \[\therefore \] Products of the roots of \[{{x}^{2}}-b.0-\sqrt{3}=0\] is \[-\sqrt{3}\]
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