A) \[-4(b+q)\]
B) \[4(b+q)\]
C) \[4(b-q)\]
D) \[4(q-b)\]
Correct Answer: A
Solution :
Let \[\alpha ,\beta \] are the roots of the equation \[{{x}^{2}}+ax-b=0\] \[\therefore \] \[\alpha +\beta =-a,\,\,\alpha \beta =-b\] and \[\gamma ,\delta \] are the roots of the equation \[{{x}^{2}}-px+q=0\] \[\therefore \] \[\gamma +\delta =p,\,\gamma \delta =q\] Given, \[\alpha -\beta =\gamma -\delta \] \[\Rightarrow \] \[{{(\alpha -\beta )}^{2}}={{(\gamma -\delta )}^{2}}\] \[\Rightarrow \] \[{{(\alpha +\beta )}^{2}}-4\alpha \beta ={{(\gamma +\delta )}^{2}}-4\gamma \delta \] \[\Rightarrow \] \[{{a}^{2}}+4b={{p}^{2}}-4q\] \[\Rightarrow \] \[{{a}^{2}}-{{p}^{2}}=-4(b+q)\]
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