Daily Math · 2026-05-16

Question 1

The discriminant of $2x^2 - 3x - 5 = 0$ equals:

Accepted Answer

$\Delta = (-3)^2 - 4 \cdot 2 \cdot (-5) = 9 + 40 = 49$.

Answer

$49$

Answer

$9$

Answer

$-31$

Answer

$29$

Question 2

The slant asymptote of $f(x) = \dfrac{2x^2 + 3x + 1}{x - 1}$ as $x 	o \pm\infty$ is:

Accepted Answer

$\dfrac{2x^2 + 3x + 1}{x - 1} = 2x + 5 + \dfrac{6}{x - 1}$. As $x 	o \pm\infty$, the remainder vanishes, leaving the slant asymptote $y = 2x + 5$.

Answer

$y = 2x$

Answer

$y = 2x + 3$

Answer

$y = 2x + 5$

Answer

$y = x + 1$

Question 3

The determinant $\det \begin{pmatrix} 1 & a & a^2 \ 1 & b & b^2 \ 1 & c & c^2 \end{pmatrix}$ equals (Vandermonde):

Accepted Answer

$\det = (b - a)(c - a)(c - b)$. (It's zero iff at least two of $a, b, c$ are equal.)

Answer

$abc$

Answer

$a + b + c$

Answer

$(b - a)(c - a)(c - b)$

Answer

$(a - b)(b - c)(c - a)$

Problems & worked solutions