Question:
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
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
Show Hint
Compare coefficients of $x$ and the constant term to find unknowns in an identity.
Updated On: Apr 26, 2026
- b = 2, c = 1
- b = 4, c = -1
- b = 1, c = 2
- b = 3, c = -1
Show Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
Step 1: Substitution
$f(x+1) = b(x+1)^2 + c(x+1) + d = b(x^2 + 2x + 1) + cx + c + d$.
$f(x+1) - f(x) = b(2x + 1) + c$.
Step 2: Equate Coefficients
$2bx + (b + c) = 8x + 3$.
$2b = 8 \implies b = 4$.
Step 3: Solve for $c$
$b + c = 3 \implies 4 + c = 3 \implies c = -1$.
Final Answer: (B)
$f(x+1) = b(x+1)^2 + c(x+1) + d = b(x^2 + 2x + 1) + cx + c + d$.
$f(x+1) - f(x) = b(2x + 1) + c$.
Step 2: Equate Coefficients
$2bx + (b + c) = 8x + 3$.
$2b = 8 \implies b = 4$.
Step 3: Solve for $c$
$b + c = 3 \implies 4 + c = 3 \implies c = -1$.
Final Answer: (B)
Was this answer helpful?
0
0
Top MHT CET Mathematics Questions
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- If $\int\frac{f\left(x\right)}{log \left(sin\,x\right)}dx = log\left[log\,sin\,x\right]+c$ then $f\left(x\right)=$
- If $\int\limits^{K}_0 \frac{dx}{2 + 18 x^2} = \frac{\pi}{24}$, then the value of K is
- If $\int^{\pi/2}_{0} \log\cos x dx =\frac{\pi}{2} \log\left(\frac{1}{2}\right)$ then $ \int^{\pi/2}_{0} \log\sec x dx = $
- The point on the curve $y = \sqrt{x - 1}$ where the tangent is perpendicular to the line $2x + y - 5 = 0 $ is
View More Questions
Top MHT CET Integral Calculus Questions
- The surface area of a spherical balloon is increasing at the rate of \( 2 \, \text{cm}^2/\text{sec} \). Then the rate of increase in the volume of the balloon, when the radius of the balloon is \( 6 \, \text{cm} \), is:
- If \( f(x) = 2x^3 - 15x^2 - 144x - 7 \), then \( f(x) \) is strictly decreasing in:
- If \( y = (\sin x)^y \), then \( \frac{dy}{dx} \) is:
- Integrate the following function w.r.t. $x$: $\int \frac{e^{3x}}{e^{3x} + 1} \, dx$
- The general solution of
$$ \left(x\frac{dy}{dx} - y\right)\sin\frac{y}{x} = x^3 e^x $$ is:
View More Questions
Top MHT CET Questions
- During r- DNA technology, which one of the following enzymes is used for cleaving DNA molecule ?
- In non uniform circular motion, the ratio of tangential to radial acceleration is (r = radius of circle, $v =$ speed of the particle, $\alpha =$ angular acceleration)
- The temperature of $32^{\circ}C$ is equivalent to
- The line $5x + y - 1 = 0$ coincides with one of the lines given by $5x^2 + xy - kx - 2y + 2 = 0 $ then the value of k is
- The heat of formation of water is $ 260\, kJ $ . How much $ H_2O $ is decomposed by $ 130\, kJ $ of heat ?
View More Questions