A) \[p=1,q=5\]
B) \[p=5,q=1\]
C) \[p=1,q=1\]
D) \[p=1,q=-1\]
E) none of these
Correct Answer: D
Solution :
\[\because \]a and b are the roots of equation \[{{x}^{2}}-3x+1=0\] \[\therefore \]\[a+b=3\]and\[ab=1\]. Now, the given roots are\[a-2\]and\[b-2\] \[\therefore \]Sum of roots \[=a-2+b-2\] \[=3-4=-1\] and product of roots\[=(a-2)(b-2)\] \[=ab-2(a+b)+4\] \[=1-6+4=-4\] \[\therefore \]Required equation is\[{{x}^{2}}+x-1=0\] which is equivalent to\[{{x}^{2}}+px+q=0\] \[\therefore \] \[p=1\] and\[q=-1\]You need to login to perform this action.
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