Recall that we can always solve a quadratic equation $ax_{2}+bx+c=0,$ by using the Quadratic Formula. $x=2a-b±b_{2}−4ac $ The quantity inside the square root $b_{2}−4ac$ is called the discriminant. Note that if it is positive, we will have two real solutions. If it is $0,$ there will be just one real solution. And, if it is negative, there will be two imaginary solutions. Hence, we can know the quantity and type of the solutions just by inspecting it.
By using the discriminant of a quadratic equation it is possible to determine the number and type of solutions of the equation. |