JAMB 1984 · UME · Q17

A straight line $y = mx$ meets the curve $y = x^2 - 12x + 40$ in two distinct points. If one of them is $(5, 5)$ , find the other.

Worked solution (try it first)

The point $(5, 5)$ is on $y = mx$ , so $5 = 5m$ and $m = 1$ .
The line is $y = x$ .
Where the line meets the curve, $x = x^2 - 12x + 40$ , so $x^2 - 13x + 40 = 0$ .
Factorise: $(x - 5)(x - 8) = 0$ , so $x = 5$ (the point you know) or $x = 8$ .
On $y = x$ , $x = 8$ gives $y = 8$ .
The other point is $(8, 8)$ , option B.