What is the result of applying the quadratic formula to a second-degree equation?

Applying the quadratic formula to a second-degree equation yields the roots, or solutions, of the equation. The quadratic formula is given as:

[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

]

where (ax^2 + bx + c = 0) is the standard form of a quadratic equation. When you substitute the coefficients (a), (b), and (c) from the specific quadratic equation into this formula, it allows you to find the values of (x) that satisfy the equation. These values are known as the roots, and they represent the points where the corresponding quadratic function intersects the x-axis on a graph.

This process does not produce a linear equation, a system of equations, or a new variable, but rather identifies the specific solutions for the variable (x) in the context of the quadratic equation. Understanding this framework highlights the role of the quadratic formula as a critical tool for solving second-degree polynomial equations.