How do I find the roots of a quadratic equation?

There are a few methods you can use. Here are two methods: 1) Inspection. Say we have the equation x²+4x+3. We can find two numbers which multiply together to make 3 but add together to make 4. Such numbers are 3 and 1 (3*1=3 and 3+1=4). So we factorise this equation and it becomes (x+1)(x+3). To find the roots we make this equation equal to 0. This means that either (x+1)=0 or (x+3)=0, which implies that the roots are x=-1 and x=-3. 2) Quadratic Formula. For more complicated equations it makes sense to use the quadratic formula. For the general case, if we have ax²+bx+c then the quadratic formula says that the roots of this equation are (-b+sqrt(b²-4ac))/2a and (-b-sqrt(b²-4ac))/2a. This works for all quadratic equations provided that b²-4ac is non-negative. The number of roots depends on the value of b²-4ac.