JAMB 1988 · UME · Q25

The figure shows the graph of $y = \frac{x^2 + 3}{x + 4}$ and the line $y = 1$ . Use it to find the solution of the equation $x^2 - x - 1 = 0$ .

Worked solution (try it first)

Where the curve meets the line $y = 1$ : $\dfrac{x^2 + 3}{x + 4} = 1$ .
Multiply by $x + 4$ : $x^2 + 3 = x + 4$ , which rearranges to $x^2 - x - 1 = 0$ .
So the roots are the $x$ -values where the line $y = 1$ cuts the curve: about $x = -0.6$ and $x = 1.6$ , option A.
Check with the formula: $x = \frac{1 \pm \sqrt5}{2}$ , which is $1.618$ or $-0.618$ .