Published by:
CGP EDU Academic Team
Published on: August 14, 2026
Let p(x) be a polynomial of degree 4 having extremum at x = 1, 2 and 
= 2. Then the value of p(2) is
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
p(x) = ax 4 + bx 3 + cx 2 + dx + e
p ′ (x) = 4ax 3 + 3bx 2 + 2cx + d
p ′ (1) = 4a + 3b + 2c + d = 0 .....(i)
p ′ (2) = 32 a + 12 b + 4c + d = 0 .....(ii)
= 2
= 2
c + 1 = 2, d = 0, e = 0
c = 1
Now equation (i) and (ii) are
4a + 3b = – 2 and 32 a + 12 b = – 4
⇒ a = 
and b = – 1
Prepare Smarter with CGP Edu
Get practice questions, solutions, and test series in one place.
Write a Review
Share your experience with this question and solution.
Commentary
Send your comment, doubt, correction, or feedback to admin.
Similar Questions
Explore conceptually related problems
For the function f(x) = x cos , x ≥ 1,
Let f be a function defined on R (the set of all real numbers) such that
f ′ (x) = 2010 (x – 2009) …
Let f, g and h be real-valued functions defined on the interval [0, 1] by f(x) = + , g(x) = + …
Match the statements given in Column-I with the intervals/union of intervals given in Column-II
Col…
The number of distinct real roots of x 4 – 4x 3 + 12x 2 + x – 1 = 0 is
Let p(x) be a real polynomial of least degree which has a local maximum at x = 1 and a local minimu…