Why do you put the quadratic equation equal to zero when you want to find it’s roots?

It is better to think of it as substituting one equation into another, rather than thinking of it as ‘making it equal to zero’. Say you have a quadratic equation y = x^2 - x - 6 and you want to find it’s roots. It’s roots are where the quadratic graph meets the line y = 0. (I would demonstrate this with a diagram). To solve this, you have two equations, so you can substitute y = 0 into y = x^2 - x - 6, to get x^2 - x - 6 = 0, which can be solved.