Find the roots for the quadratic equation x^(2)+6x+5=0

For this question I would consider different methods for finding the roots of quadratics and remind the student that an exam could ask for a particular method to be used (as on one of the recent GCSE maths papers for AQA).factorising: I would state inorder to find the values we use for factorising. We need two numbers that both multiply to give 5 (the product), while they also can be added together to give 6 (the sum). Here 5 and 1 satisfy the conditions, so the factorised equation looks like (x+5)(x+1)=0. The only numbers x can be to satisfy the equation are both -5 and -1.quadratic formula: Next, I would write the quadratic formula, x=(-b+-sqrt(b^(2)-4ac))/(2*a). Where a=1, b=6, c=5. The resulting answers will be -5 and -1.Completing the Square: Finally I would walk through the most complicated way of solving a quadratic (to students). x^(2)+6x+5=0 <=> (x+3)^(2)-(3)^(2)+5=0 <=> (x+3)^(2)=4 <=> x+3=+-sqrt(4) <=> x=-3+-2. Therefore, the roots are x=-5 and x=-1