Find the roots of the equation: x^2-2x-3=0

The point at which the explanation of the solution is started, will depend on the level of understanding of the student and previous knowledge on the subjectA root is a numerical value that represents the solution of the equation so that if substituted in the place of x, will make the equation true.This equation involves a polynomial function which is a function of an independent variable (x in this case). In simple terms, this is a summation of x terms with different powers. The number of roots of the equation is equal to the order of the polynomial which is the highest power term of the independent variable. In this case the highest power term is x^2 therefore the order of the polynomial is 2 and there are 2 roots to this equation. The approach to solving this equation, is to rearrange the left hand side of the equation so that it is in a form of a product of two terms. This is done because if xy=0, we know that either x or y (or both) must be 0 for this to be true. We therefore need to factorise the left hand side to be in the form (x+a)(x+b) = 0. If we expand this factorisation we get x^2+x(a+b)+ab=0. Comparing this result to the equation we have to solve, we can see that -2 corresponds to the term (a+b) and -3 to the term ab. We therefore need to find values of a and b to make this true. allow student to find a and b. The solution is that a=1 and b=-3 or vise versa. Therefore the factorised equation would now be (x+1)*(x-3)=0. allow student to reach solution if he can from this point. For this to be true, either (x+1) or (x-3) must be 0. The two roots of the equation are: x=-1 and x=3.