Question
Let S = \ x^ 3 +a x^ 2 +b x+c: a, b, c ~N . and .a, b, c 20 \ be a set of polynomials. Then the number of polynomials in S, which are divisible by x^ 2 +2, is
JEE Main
Mathematics
Quadratic Equation
2026
JEE Main 2026 (28 January Shift 1)
JEE Main Mathematics Question (2026) — Solution
Options
- A. 10
- B. 20
- C. 6
- D. 120
Answer
A. 10
Step-by-step solution
If x^2 + 2 divides x^3 + ax^2 + bx + c, write x^3 + ax^2 + bx + c = (x^2 + 2)(x + k). Expanding: x^3 + kx^2 + 2x + 2k. Comparing coefficients: a = k, b = 2, c = 2a. Constraints: a N , a 20, and c = 2a 20 a 10. So a \ 1, 2, 3, ..., 10\ , giving 10 polynomials.
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