(A) 6

(B) 120

(C) 20

(D) 10

Correct Answer: 10

Explanation

If a polynomial is divisible by x² + 2, then it must be of the form:

(x² + 2)(x + k)

where k is a constant.

Expanding:

(x² + 2)(x + k) = x³ + kx² + 2x + 2k

Comparing with the given polynomial:

x³ + ax² + bx + c

we get:

a = k,   b = 2,   c = 2k

Given that:

a, b, c ∈ N and a, b, c ≤ 20

Since b = 2, this condition is satisfied.

Now for c = 2k ≤ 20:

k ≤ 10

Also k ∈ N, so:

k = 1, 2, 3, ..., 10

Total possible values of k = 10

Therefore, number of required polynomials = 10

Related JEE Main Questions