JEE WhatsApp Group
Sign in
Please select an account to continue using cracku.in
↓ →
JEE WhatsApp Group
Join Our JEE Preparation Group
Prep with like-minded aspirants; Get access to free daily tests and study material.
Let $$S=\left\{x^{3}+ax^{2}+bx+c:a,b,c, \in N \text{ and }a,b,c \leq 20\right\}$$ be a set of polynomials. Then the number of polynomials in S, which are divisible by $$x^{2}+2$$, is
If $$x^2 + 2$$ divides $$x^3 + ax^2 + bx + c$$, then:
$$x^3 + ax^2 + bx + c = (x^2 + 2)(x + a) = x^3 + ax^2 + 2x + 2a$$
Comparing coefficients:
$$b = 2$$ and $$c = 2a$$
$$b = 2$$ (fixed, and $$2 \leq 20$$ ✓)
$$c = 2a$$, with $$c \leq 20$$ and $$a \leq 20$$
$$2a \leq 20 \implies a \leq 10$$
Also $$a \geq 1$$
So $$a$$ can be 1, 2, 3, ..., 10 → 10 values.
Therefore, the number of polynomials is Option 1: 10.
Click on the Email ☝️ to Watch the Video Solution
Create a FREE account and get:
Educational materials for JEE preparation
Ask our AI anything
AI can make mistakes. Please verify important information.
AI can make mistakes. Please verify important information.
