Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The number of polynomials of the form x 3 + ax 2 + bx + c( 
a,b, c 
{1, 2, 3…10}) which are divisible by x 2 + 1 is equal to
Text Solution
Verified by ExpertsThe correct answer is:
B
f (x) = x 3 + ax 2 + bx + c is divisible by x 2 + 1 or (x + i) (x - i)
So, f(i) = 0 and f(-i) = 0
f(i) = 0 
i 3 + ai 2 + bi + c = 0
-i - a + bi + c = 0
(c - a) + i (b - 1) = 0 
c = a, b = 1
f (-i) = 0 
(- i) 3 + a(- i) 2 + b (-i) + c = 0
i - a - ib + c = 0
(c - a) - i (b - 1) = 0 
c = a, b = 1
B =1 and c = a
10 polynomials are possible
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