JAMB 1984 · UME · Q23

The quadratic equation whose roots are $1 - \sqrt{13}$ and $1 + \sqrt{13}$ is

Worked solution (try it first)

The sum of the roots is $(1 - \sqrt{13}) + (1 + \sqrt{13}) = 2$ .
The product is a difference of two squares: $(1 - \sqrt{13})(1 + \sqrt{13}) = 1 - 13$
$= -12$ .
The equation is $x^2 - (\text{sum})x + (\text{product}) = 0$ , which is $x^2 - 2x - 12 = 0$ , option E.