Daily Math · 2026-05-20

Question 1

For which value of $a$ is $(a, 1, 2) \perp (3, -1, -1)$?

Accepted Answer

$3a - 1 - 2 = 0 \Rightarrow 3a = 3 \Rightarrow a = 1$.

Answer

$0$

Answer

$1$

Answer

$-1$

Answer

$3$

Question 2

The polynomial $P(x) = x^3 + x + 1$ has exactly:

Accepted Answer

$P'(x) > 0$ everywhere, so $P$ is strictly increasing on $\mathbb{R}$. Combined with $\lim_{\pm\infty}P = \pm\infty$, $P$ has exactly one real root by IVT.

Answer

$1$ real root

Answer

$2$ real roots

Answer

$3$ real roots

Answer

$0$ real roots

Question 3

$\arg\!\left(\dfrac{1+i}{1-i}\right)$ (in $(-\pi, \pi]$) equals:

Accepted Answer

$\dfrac{1+i}{1-i} = \dfrac{(1+i)^2}{(1-i)(1+i)} = \dfrac{2i}{2} = i$, whose argument is $\dfrac{\pi}{2}$.

Answer

$	frac{\pi}{2}$

Answer

$	frac{\pi}{4}$

Answer

$0$

Answer

$\pi$

Problems & worked solutions

Problem 1 — 3D Coordinate Geometry

Problem 2 — Rolle's Sign Method

Problem 3 — Complex numbers