MHT CET · Maths · Functions
The values of b and c for which the identity \(\mathrm{f}(x+1)-\mathrm{f}(x)=8 x+3\) is satisfied, where \(\mathrm{f}(x)=\mathrm{b} x^2+\mathrm{c} x+\mathrm{d}\), are
- A \(b=2, c=1\)
- B \(b=4, c=-1\)
- C \(b=1, c=2\)
- D \(b=3, c=-1\)
Answer & Solution
Correct Answer
(B) \(b=4, c=-1\)
Step-by-step Solution
Detailed explanation
\(f(x+1) = b(x+1)^2 + c(x+1) + d = b(x^2+2x+1) + cx+c+d = bx^2+(2b+c)x+b+c+d\) \(f(x+1)-f(x) = (bx^2+(2b+c)x+b+c+d) - (bx^2+cx+d) = 2bx+b+c\)
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