JAMB 1986 · UME · Q30

At what points does the straight line $y = 2x + 1$ intersect the curve $y = 2x^2 + 5x - 1$ ?

Worked solution (try it first)

Where they meet, $2x^2 + 5x - 1 = 2x + 1$ .
Bring everything to one side: $2x^2 + 3x - 2 = 0$ .
Factorise: $(2x - 1)(x + 2) = 0$ , so $x = \frac12$ or $x = -2$ .
Find $y$ from the line $y = 2x + 1$ : $x = \frac12$ gives $y = 2$ , and $x = -2$ gives $y = -3$ .
So the points are $(-2, -3)$ and $(\frac12, 2)$ , option A.