Here are the essential concepts you must grasp in order to answer the question correctly.
Completing the Square
Completing the square is a method used to solve quadratic equations by transforming the equation into a perfect square trinomial. This involves rearranging the equation and adding a specific value to both sides to create a binomial squared. This technique simplifies the process of finding the roots of the equation.
Recommended video:
Solving Quadratic Equations by Completing the Square
Quadratic Equation
A quadratic equation is a polynomial equation of the form ax² + bx + c = 0, where a, b, and c are constants, and a ≠ 0. The solutions to this equation can be found using various methods, including factoring, using the quadratic formula, or completing the square. Understanding the standard form is crucial for applying these methods effectively.
Recommended video:
Introduction to Quadratic Equations
Discriminant
The discriminant is a component of the quadratic formula, given by the expression b² - 4ac. It determines the nature of the roots of a quadratic equation: if the discriminant is positive, there are two distinct real roots; if it is zero, there is one real root; and if negative, the roots are complex. Analyzing the discriminant helps in understanding the solutions' characteristics.
Recommended video: