Without solving the equation,determine the nature of its roots. 1.x^2-x-12=0​

Step-by-step explanation:Let's analyze the quadratic equation \(x^2 - x - 12 = 0\) without solving for the roots.The nature of the roots depends on the discriminant \(D\), given by:\[D = b^2 - 4ac\]where the quadratic is in the form \(ax^2 + bx + c = 0\).Here:- \(a = 1\)- \(b = -1\)- \(c = -12\)Calculate the discriminant:\[D = (-1)^2 - 4 \times 1 \times (-12) = 1 + 48 = 49\]Since \(D = 49 > 0\), the roots are **real and distinct**.**Answer:** The quadratic has **two real and distinct roots**.

Answered by jhoyax17 | 2025-08-06