Mathematics - Quadratic Equation Question with Solution | TestHub

Because $f(x+1)-f(x)=8x+3$.

$$\begin{array}{rl}& \Rightarrow \left\{b(x+1{)}^2+c(x+1)+d\right\}-\left\{b{x}^2+cx+d\right\}=8x+3\\ & \Rightarrow b\left\{(x+1{)}^2-x^2\right\}+c=8x+3\\ & \Rightarrow b(2x+1)+c=8x+3\\ & Oncomparing,\\ & Then,2b=8andb+c=3\\ & Thus,b=4andc=-1\end{array}$$