The solutions x = 2 and x = -1 to the quadratic equation x² - x - 2 = 0 can reveal something very neat indeed.
We can rearrange x = 2 into x - 2 = 0.
Similarly we can rearrange x = -1 into x + 1 = 0
We can write these as:
If we multiply the bracketed terms, we get: (x - 2)(x + 1) = 0
Multiplying out the brackets: x² - 2x + x - 2 = 0
What this means is important: quadratic equations can be factorised, offering a reasonably quick solution.