A) \[3{{x}^{2}}-5x-100=0\]
B) \[5{{x}^{2}}+3x+100=0\]
C) \[3{{x}^{2}}-5x+100=0\]
D) \[3{{x}^{2}}+5x-100=0\]
E) \[5{{x}^{2}}-3x-100=0\]
Correct Answer: A
Solution :
\[\because \]\[3{{p}^{2}}=5p+2\] \[\Rightarrow \] \[p=2,-\frac{1}{3}\] and \[3{{q}^{2}}=5q+2\] \[\Rightarrow \] \[q=2,-\frac{1}{3}\] \[\because \] \[p\ne q,\] \[\therefore \] assume that \[p=2\]and \[q=-\frac{1}{3}\] Now, the given roots of equation are \[(3p-2q)\]and\[(3q-2p)\]i.e., \[\left( \frac{20}{3},-5 \right)\] Sum of roots\[=\frac{20}{3}-5=\frac{5}{3}\] and product of roots\[=\frac{20}{3}\times (-5)=-\frac{100}{3}\] \[\therefore \]Required equation is \[{{x}^{2}}-\frac{5}{3}x-\frac{100}{3}=0\] \[\Rightarrow \] \[3{{x}^{2}}-5x-100=0\]
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