A) \[b=2,\,c=1\]
B) \[b=4,c=-1\]
C) \[b=-1,c=4\]
D) \[b=-1,c=1\]
Correct Answer: B
Solution :
We have, \[f(x)=b{{x}^{2}}+cx+d\] \[f(x+1)=b{{(x+1)}^{2}}+c(x+1)+d\] Give that \[f(x+1)-f(x)=8x+3\] \[\Rightarrow \] \[b{{(x+1)}^{2}}+c(x+1)+d\] \[\Rightarrow \] \[-(b{{x}^{2}}+cx+d)=8x+3\] \[\Rightarrow \] \[b({{x}^{2}}+1+2x)+c(x+1)+d\] \[-(b{{x}^{2}}+cx+d)=8x+3\] \[\Rightarrow \] \[2bx+(b+c)=8x+3\] On comparing the coefficient of \[x\]and constant \[2b=8,\,b+c=3\] \[\Rightarrow \] \[b=4,\,c=-1\]
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