Here are the essential concepts you must grasp in order to answer the question correctly.
Quadratic Formula
The quadratic formula is a method for solving quadratic equations of the form ax^2 + bx + c = 0. It is expressed as x = (-b ± √(b² - 4ac)) / (2a), where a, b, and c are coefficients from the equation. This formula provides the solutions (roots) of the equation, which can be real or complex depending on the value of the discriminant (b² - 4ac).
Recommended video:
Solving Quadratic Equations Using The Quadratic Formula
Standard Form of a Quadratic Equation
A quadratic equation is typically written in standard form as ax^2 + bx + c = 0, where a, b, and c are constants, and a ≠ 0. This form is essential for identifying the coefficients needed to apply the quadratic formula. In the given equation, it is necessary to rearrange the terms to achieve this standard form before solving.
Recommended video:
Converting Standard Form to Vertex Form
Discriminant
The discriminant is the part of the quadratic formula under the square root, calculated as b² - 4ac. It determines the nature of the roots of the quadratic equation: if the discriminant is positive, there are two distinct real roots; if it is zero, there is one real root (a repeated root); and if it is negative, the roots are complex. Understanding the discriminant helps predict the solutions' characteristics.
Recommended video: