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Mathematics · Quadratic Equations

JEE Main 2026 — 28 January, Morning Shift — Question 8

Let S={x3+ax2+bx+c:a,b,c∈NS=\left\{x^{3}+a x^{2}+b x+c: a, b, c \in N\right. and a,b,c≤a, b, c \leq 20 } be a set of polynomials. Then the number of polynomials in S , which are divisible by x2+2\mathrm{x}^{2}+2, is

  1. Option A:

    20

  2. Option B:

    6

  3. Option C:

    120

  4. Option D:

    10

    Correct

Answer: D

Step-by-step solution

x3+ax2+bx+c=(x2+2)(x+c2)x^{3}+a x^{2}+b x+c=\left(x^{2}+2\right)\left(x+\frac{c}{2}\right)

x2:a=c2x^{2}: a=\frac{c}{2}

x:b=2x: b=2

b=2,a=c2,c∈{2,4,…,20}b=2, a=\frac{c}{2}, c \in\{2,4, \ldots, 20\}

Number of polynomials in′S′ ' S ' will be 10.10.

Answer key and solution verified before publishing.

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Exam
JEE Main 2026
Paper
28 January, Morning Shift
Subject
Mathematics
Chapter
Quadratic Equations
Topic
Theory of Quadratic Equations

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