what is the answer of the nature of the roots​

Step-by-step explanation:The "nature of the roots" refers to the type or characteristics of the solutions (roots) of a quadratic equation or polynomial. It is typically determined by the discriminant (D) of the quadratic equation \(ax^2 + bx + c = 0\), where \(D = b^2 - 4ac\).Here's how the discriminant relates to the nature of roots:1. **If \(D > 0\):** The quadratic has **two real and distinct roots**.2. **If \(D = 0\):** The quadratic has **two real and equal roots** (also called repeated roots).3. **If \(D < 0\):** The quadratic has **two complex conjugate roots** (no real roots).**Summary table:**| Discriminant (D) | Nature of Roots ||------------------|-------------------------------------|| \(D > 0\) | Two real and distinct roots || \(D = 0\) | Two real and equal roots || \(D < 0\) | Two complex conjugate roots |

Answered by jhoyax17 | 2025-08-06