If the graph of the function f(x) = ax 3 + x 2 + bx + c is …

Maths Functions, Limits, Continuity and Differentiability NTA Abhiyas Question - Function Single Correct MCQ

Published on: August 13, 2026

If the graph of the function f(x) = ax 3 + x 2 + bx + c is symmetric about the line x = 2, then the value of a + b is equal to

-4

-10

Text Solution

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The correct answer is:

-4

f(x) is symmetric about the line x = 2

f(2 + x) = f(2-x)

a(2 + x) 3 + (2 + x) 2 + & (2 + x) + c = a(2 - x) 3 + (2 - x) 2 + & (2 - x) + c

a { (2 + x) 3 - (2 - x) 3 } + {(2 + x) 2 - (2 - x) 2 } + b{(2 + x) - (2 - x)} = 0

a{(8 + 12x + 6x 2 + x 3 ) - (8 - 12x + 6x 2 - x 3 )} + 2 (4x) + 6(2x) = 0

a (24x + 2x 3 ) + 8x + 2bx = 0

2ax 3 + (24a + 2b + 8)x = 0

Which must be true

it is an identity

2a = 0,24a + 2b + 8 = 0

a= 0, 26 + 8 = 0

b=-4

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