Final answer:
A quadratic equation can sometimes have imaginary roots, which depends on the discriminant found in the quadratic formula. If the discriminant is negative, the equation has two imaginary roots.
Step-by-step explanation:
A quadratic equation can sometimes have imaginary roots. This is determined by the discriminant which is found in the quadratic formula √x²+bx+c = 0. The discriminant is part of the formula under the square root, calculated as b²-4ac. If the discriminant is positive, the equation has two real and distinct roots. If it is zero, it has one real root (also known as a repeated or double root). However, if the discriminant is negative, the quadratic equation will have two imaginary or complex roots.
In practical applications, such as Two-Dimensional (x-y) Graphing, especially when constructed on physical data, quadratic equations tend to have real roots. Real roots are more meaningful in most real-world applications since they can represent measurable quantities. For example, when dealing with equilibrium problems, we often seek real, positive roots for meaningful solutions.