How do I find the roots of a quadratic equation?

A quadratic equation is an equations of the form:   ax² + bx + c = 0 (1)  where a is not 0. The ways of finding the roots are:  quadratic formula, factorising, substituting, completing the square.

Today, I'll cover solution by factorising, which is best understood with an example. Let's try to factorise: X² - 7x + 12 = 0.

Firstly, we look at the last term, the 'c' in (1), which is a 12. Which two factors will give 12 when multiplied? Our options are: ±(1,12), ±(2,6), ±(3,4).

Which of these pairs will give -7 when ADDED together? (We use -7 because that is the 'b' in this equation, and we ADD because 'c' is positive in this equation. If 'b' were positive and 'c' negative we would say: Which of these pairs will give 7 when SUBTRACTED from each other?)

Our only option is: -(3,4). Therefor  X² - 7x + 12 = (x - 3)(x - 4) = 0.

So either (x-3) = 0 or (x-4) = 0. So the roots are X = 3 and x = 4. A question now: with these roots, which of these statements is true? b² - 4ac >, <, = 0.