What are Distinct Roots in Maths?

Distinct roots in mathematics pertain to the solutions of a polynomial equation that are unique and non-repeating. For a quadratic equation ax²+bx+c=0, the discriminant (b²−4ac) determines the nature of the roots. If the discriminant is positive, the equation has two distinct real roots. The quadratic formula x = (−b ± b²−4ac)​​/2a expresses these roots, where the ±± symbol indicates the two solutions.

For example, consider the quadratic equation x²−4=0. The discriminant is (−4), and applying the quadratic formula yields two distinct real roots: x = 2 and x = -2.

Distinct roots are significant in various mathematical and practical applications. They signify the points where a polynomial equation intersects the x-axis on a graph, providing unique solutions to problems in physics, engineering, and other fields. The concept contrasts with repeated or imaginary roots, emphasizing the individuality and separateness of each solution.