What are the roots of y=x^2+5x+6 ?

Roots = where line touches x-axis. Set equation equal to 0 as y=0 at the x-axis. Now we need to solve for the x values at which y=0. Quadratic is now 0=x^2+5x+6. Factorise quadratic: 0=(x+3)(x+2). Now you can divide the zero by either (x+3) or (x+2). Both are possibilities and cannot be ignored. Hence two equations are 0=x+3 and 0=x+2. Rearrange now to find that x=-3 and x=-2 when y=0. You have now found the roots of the equation.