JEE Main 2021 — Definite Integration Question with Solution
From: JEE Main 2021 (Online) 18th March Evening Shift
Question
Let P(x) be a real polynomial of degree 3 which vanishes at x = 3. Let P(x) have local minima at x = 1, local maxima at x = 1 and = 18, then the sum of all the coefficients of the polynomial P(x) is equal to _________.
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Show full solutionCorrect answer: 8
Correct answer
8
Step-by-step explanation
P'(x) = a(x + 1)(x 1)
P(x) = ax + C
P(3) = 0 (given)
a(9 + 3) + C = 0
6a = C ..... (i)
Also,
from (i)
Sum of co-efficient
= = 1 + 9 = 8
P(x) = ax + C
P(3) = 0 (given)
a(9 + 3) + C = 0
6a = C ..... (i)
Also,
from (i)
Sum of co-efficient
= = 1 + 9 = 8
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