A root of a function is where the function equals zero. So to begin to solve we must set the function to equal zero.x^2-5x+6 = 0If the question didn't make it clear already, you should be able to identify that this should have two different solutions (there are two values of x where y is zero). This is because the function is a quadratic, and we know from the sketch of a quadratic that the maximum number of roots is two.The next step is to factorise. When we factorise we put the equation into two brackets. With quadratic equations, they often take the form Ax^2+Bx+C, when a = 1 (as in this example) in order to factorise you simple find two factors of the C term which add to give the B term.Factors of 6: 6 and 1, 3 and 2, -3 and -2We can identify that -3 and -2 add to give -5 and multiply to give 6.Therefore : x^2-5x+6 = (x-3)(x-2)You can test your factorising is correct by expanding the brackets.

Finally, as we said before the roots are where the function is equal to zero and there should be two values of x.(x-3)(x-2) = 0 You can see that this is equal to zero when either of the brackets is equal to zero. Therefore set each bracket equal to zero to find the x values.x-3 = 0 , x=3x-2 = 0 , x=2