A) \[5{{x}^{2}}-3x-100=0\]
B) \[5{{x}^{2}}+3x+100=0\]
C) \[3{{x}^{2}}-5x+100=0\]
D) \[3{{x}^{2}}+5x-100=0\]
E) \[3{{x}^{2}}-5x-100=0\]
Correct Answer: E
Solution :
Given that, \[3{{p}^{2}}-5p-2=0\] \[\Rightarrow \] \[(3p+1)(p-2)=0\] \[\Rightarrow \] \[p=-\frac{1}{3},2\] and \[3{{q}^{2}}-5q-2=0\] \[\Rightarrow \] \[(3q+1)\,(q-2)=0\] \[\Rightarrow \] \[q=\frac{-1}{3},\,2\] Since, \[p\ne q\Rightarrow p=-\frac{1}{3},q=2\] Now, \[(3p-2q)=-1-4=-5\] and \[(3p-2p)=6+\frac{2}{3}=\frac{20}{3}\] \[\therefore \]Equation is \[{{x}^{2}}-\left( -5+\frac{20}{3} \right)x+\frac{(-5)(20)}{3}=0\] \[\Rightarrow \] \[3{{x}^{2}}-5x-100=0\]
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