(B) Given $f(x) = bx^2 + cx + d$. Then $f(x+1) = b(x+1)^2 + c(x+1) + d = b(x^2 + 2x + 1) + cx + c + d = bx^2 + 2bx + b + cx + c + d$. Now,$f(x+1) - f(

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(B) Given $f(x) = bx^2 + cx + d$. Then $f(x+1) = b(x+1)^2 + c(x+1) + d = b(x^2 + 2x + 1) + cx + c + d = bx^2 + 2bx + b + cx + c + d$. Now,$f(x+1) - f(x) = (bx^2 + 2bx + b + cx + c + d) - (bx^2 + cx + d) = 2bx + b + c$. We are given the identity $f(x+1) - f(x) = 8x + 3$. Comparing the coefficients of $x$ and the constant terms: $2b = 8 \implies b = 4$. $b + c = 3 \implies 4 + c = 3 \implies c = -1$. Thus,the values are $b = 4$ and $c = -1$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Relation between roots and coefficients

Medium

The values of $b$ and $c$ for which the identity $f(x+1)-f(x)=8x+3$ is satisfied,where $f(x)=bx^2+cx+d$,are

MHT CET 2025 All MHT CET

A
$b=2, c=1$
B
$b=4, c=-1$
C
$b=1, c=2$
D
$b=3, c=-1$

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4-2.Quadratic Equations and Inequations

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Relation between roots and coefficients

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