A) \[8{{x}^{2}}-10x+2=0\]
B) \[{{x}^{2}}-5x+4=0\]
C) \[2{{x}^{2}}-5x+2=0\]
D) \[{{x}^{2}}-10x+6=0\]
E) none of the above
Correct Answer: B
Solution :
Let the roots of the equation\[2{{x}^{2}}-5x+2=0\] are\[\alpha \]and\[\beta \]. Then \[\alpha +\beta =\frac{5}{2}\]and\[\alpha \beta =1\] Now, the roots of required equation be\[2\alpha \] and\[2\beta \]. \[\therefore \]Sum of roots\[=2(\alpha +\beta )=5\] and product of roots\[=2\alpha .2\beta \] \[=4\alpha \beta \] \[=4\] \[\therefore \]Required equation is \[{{x}^{2}}-5x+4=0\]
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