Daily Math · 2026-05-15

Question 1

For $A = X^2 + 3X - 1$ and $B = 2X^2 - X + 4$, the polynomial $A + B$ equals:

Accepted Answer

Add coefficients: $(1+2)X^2 + (3-1)X + (-1+4) = 3X^2 + 2X + 3$.

Answer

$X^2 + 2X + 3$

Answer

$3X^2 + 4X + 5$

Answer

$3X^2 + 2X + 3$

Answer

$-X^2 + 4X - 5$

Question 2

The number of distinct real roots of $P(x) = x^3 - 3x + 1$ is:

Accepted Answer

$P(-\infty) = -\infty$, $P(-1) = -1 + 3 + 1 = 3 > 0$, $P(1) = 1 - 3 + 1 = -1 < 0$, $P(\infty) = +\infty$. The sign sequence $-,\,+,\,-,\,+$ shows three sign changes, hence three distinct real roots.

Answer

$1$

Answer

$2$

Answer

$3$

Answer

$0$

Question 3

$(\mathbb{Z}_n, +, \cdot)$ is a field iff:

Accepted Answer

$\mathbb{Z}_n$ is a field iff every non-zero element is invertible, iff every element from $1$ to $n - 1$ is coprime to $n$, iff $n$ is prime.

Answer

$n$ is even

Answer

$n \ge 5$

Answer

$n$ is prime

Answer

$n = n!$

Problems & worked solutions

Problem 1 — Polynomials in ℂ

Problem 2 — Rolle's Sign Method

Problem 3 — Modular Arithmetic (ℤₙ)