For the function given by f(x) = x² - 5x - 6, solve for f(x)=0 by factorising.

This is a very common question for GCSE maths students and the idea of a quadratic comes up very often in other forms too.To factorise this equation we need to find two numbers whose sum is -5 and whose product is -6. By inspection, we see that -6, and +1 work. This specific equation can occasionally cause problems for students as if you rush they may think +/-2 and +/-3 could work. If we were given f(x) = x² -5x + 6 then of course -2, -3 would be the numbers we want.For the equation we are given though, we can now use the factorised form (x-6)(x+1) = 0 to see that x = 6 and x = -1 are the only solutions by setting x-6 = 0 and x+1 = 0.