Applications of Quadratic Equations

Understanding Quadratic Equations

A quadratic equation is an equation of the form $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants, and $a \neq 0$. These equations can be solved using various methods such as factorization, completing the square, or using the quadratic formula.

In this section, we will focus on solving quadratic equations using factorization and applying them to real-world problems.

Solving Quadratic Equations by Factorization

• Write the quadratic equation in the standard form $ax^2 + bx + c = 0$.
• Factorize the quadratic expression into two binomials.
• Set each factor equal to zero and solve for $x$.

For example, to solve $x^2 - 5x + 6 = 0$:

• Factorize: $(x - 2)(x - 3) = 0$
• Set each factor to zero: $x - 2 = 0$ or $x - 3 = 0$
• Solve: $x = 2$ or $x = 3$

Applications of Quadratic Equations

Quadratic equations are used in various real-life situations, such as calculating areas, determining the trajectory of objects, and solving problems involving motion.

Example Problem

A rectangular garden has an area of 48 square meters. The length is 2 meters more than the width. Find the dimensions of the garden.