Basic Technical Mathematics, 11th Edition

7.1 Quadratic Equations; Solution by Factoring

• General Quadratic Equation • Solutions of a Quadratic Equation • Solving a Quadratic Equation by Factoring • Equations with Fractions

Given that a, b, and c are constants $(a\hspace{0.17em}\ne \hspace{0.17em}0)\hspace{0.17em},\hspace{0.17em}$ the equation

$$a{x}^2\hspace{0.17em}+\hspace{0.17em}bx\hspace{0.17em}+\hspace{0.17em}c\hspace{0.17em}=\hspace{0.17em}0$$(7.1)

is called the general quadratic equation in x. The left side of Eq. (7.1) is a polynomial function of degree 2. This function, $f(x)\hspace{0.17em}=\hspace{0.17em}a{x}^2\hspace{0.17em}+\hspace{0.17em}bx\hspace{0.17em}+\hspace{0.17em}c\hspace{0.17em},\hspace{0.17em}$ is known as the quadratic function. Any equation that can be simplified and then written in the form of Eq. (7.1) is a quadratic equation in one unknown.

Among the applications of quadratic equations and functions are the following examples: In finding the flight time t of a projectile, the equation $s_0\hspace{0.17em}+\hspace{0.17em}{v}_{0}t\hspace{0.17em}-\hspace{0.17em}16t^2\hspace{0.17em}=\hspace{0.17em}0$ occurs; in analyzing ...