A) \[1,-1\]
B) \[1,\,\,1\]
C) \[-1,-1\]
D) \[1,0\]
Correct Answer: C
Solution :
\[\sqrt{\frac{5}{3}}\] and \[-\sqrt{\frac{5}{3}}\] are the zeroes of polynomial \[f(x)\] \[\therefore \] \[\left( x-\sqrt{\frac{5}{3}} \right),\,\left( x+\sqrt{\frac{5}{3}} \right)\] are factors of .i.e., \[\left( {{x}^{2}}-\frac{5}{3} \right)\] exactly divides f(x). Now, \[3{{x}^{4}}+6{{x}^{3}}-2{{x}^{2}}-10x-5\] \[=\left( {{x}^{2}}-\frac{5}{3} \right)\,(3{{x}^{2}}+6x+3)=3\left( {{x}^{2}}-\frac{5}{3} \right){{(x+1)}^{2}}\] For zeroes of polynomial f(x), \[f(x)=0\] \[\Rightarrow \] \[3\left( {{x}^{2}}-\frac{5}{3} \right){{(x+1)}^{2}}=0\] \[\Rightarrow \] \[x=\sqrt{\frac{5}{3}},\] \[-\sqrt{\frac{5}{3}},-1,-1\]
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