The slant asymptote of f(x) = (2x^2 + 3x + 1)/(x - 1) as x → ±∞ is:

(2x^2 + 3x + 1)/(x - 1) = 2x + 5 + (6)/(x - 1). As x → ±∞, the remainder vanishes, leaving the slant asymptote y = 2x + 5.

Daily Math Problems — May 16, 2026: Quadratic Function, Calculus, Determinants

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Problems & worked solutions

RO M1

Problem 1 — Quadratic Function

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

Show answer & worked solution

A. $49$ ✓ correct
B. $9$
C. $- 31$
D. $29$

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

RO M1

Problem 2 — Asymptotes

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

Show answer & worked solution

A. $y = 2 x$
B. $y = 2 x + 3$
C. $y = 2 x + 5$ ✓ correct
D. $y = x + 1$

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

RO M1

Problem 3 — Determinants

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

Show answer & worked solution

A. $a b c$
B. $a + b + c$
C. $(b - a) (c - a) (c - b)$ ✓ correct
D. $(a - b) (b - c) (c - a)$

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

Problems & worked solutions

RO M1

Problem 1 — Quadratic Function

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

Show answer & worked solution

A. $49$ ✓ correct
B. $9$
C. $- 31$
D. $29$

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

RO M1

Problem 2 — Asymptotes

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

Show answer & worked solution

A. $y = 2 x$
B. $y = 2 x + 3$
C. $y = 2 x + 5$ ✓ correct
D. $y = x + 1$

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

RO M1

Problem 3 — Determinants

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

Show answer & worked solution

A. $a b c$
B. $a + b + c$
C. $(b - a) (c - a) (c - b)$ ✓ correct
D. $(a - b) (b - c) (c - a)$

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