The nature of roots refers to the type of roots that a quadratic equation has. A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are real numbers and a is not equal to 0. The nature of roots can be determined by calculating the discriminant, which is given by the formula b^2 - 4ac. Depending on the value of the discriminant, the nature of roots can be classified as follows:

• If the discriminant is greater than 0, then the equation has two real and distinct roots.
• If the discriminant is equal to 0, then the equation has one real and repeated root.
• If the discriminant is less than 0, then the equation has no real roots, but it has two complex roots.

The nature of roots can also be determined by using the quadratic formula, which is given by (-b ± sqrt(b^2 - 4ac)) / 2a. The term inside the square root is the discriminant, and the sign of the discriminant determines the nature of roots. If the discriminant is positive, then the roots are real and distinct. If the discriminant is zero, then the roots are real and repeated. If the discriminant is negative, then the roots are complex conjugates.

In summary, the nature of roots of a quadratic equation can be real and distinct, real and repeated, or complex conjugates, depending on the value of the discriminant.