JEE Main202628 January 2026Morning ShiftMathematicsQuadratic EquationActual

Let S = x³+a x²+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 x²+2 , is

Options

A10
B20
C6
D120

Correct 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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