A) \[\frac{2}{\sqrt{3}},\frac{\sqrt{3}}{4}\]
B) \[-\frac{2}{\sqrt{3}},\frac{\sqrt{3}}{4}\]
C) \[\frac{2}{\sqrt{3}},-\frac{\sqrt{3}}{4}\]
D) \[-\frac{2}{\sqrt{3}},-\frac{\sqrt{3}}{4}\]
Correct Answer: B
Solution :
| Let \[p\left( x \right)=4\sqrt{3}{{x}^{2}}+5x-2\sqrt{3}\] |
| \[=4\sqrt{3}{{x}^{2}}+\left( 8-3 \right)x-2\sqrt{3}\] |
| [by splitting middle term] |
| \[=4\sqrt{3}{{x}^{2}}+8x-3x-2\sqrt{3}\] |
| \[=4x\left( \sqrt{3}x+2 \right)-\sqrt{3}\left( \sqrt{3}x+2 \right)\] |
| \[=\left( 4x-\sqrt{3} \right)\left( \sqrt{3}x+2 \right)\] |
| For finding the zeroes, put \[p\left( x \right)=0\] |
| \[\therefore \,\,\,\left( 4x-\sqrt{3} \right)\left( \sqrt{3}x+2 \right)=0\] |
| \[\Rightarrow \,\,\,\,4x-\sqrt{3}=0\] and \[\sqrt{3}x+2=0\] |
| \[\Rightarrow \,\,\,x=\frac{\sqrt{3}}{4}\] and \[x=-\frac{2}{\sqrt{3}}\] |
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