Solving Quadratic Equations

Quadratic Equation in One Variable: ax² + bx + c = 0, where a, b and c are real numbers with a ≠ 0. We will solve these equations by several methods.

 

I. Solving Quadratic Equations by Factoring

The Zero Product Property: ab = 0 if and only if either a = 0 or b = 0 or both a and b equal zero.

 

II. Graphical Solution

Once the equation is written in the form ax² + bx + c = 0, we can graph the left side as y₁ and find the x- intercepts. These x-intercepts or zeros of the function are the solutions to the quadratic equation ax² + bx + c = 0.

 

III. Square Root Property

The solution set of x² = k is:

 

IV. Using the Quadratic Formula to Solve Quadratic Equations

If ax² + bx + c = 0,  a ≠ 0, then:

 

b² - 4ac is called the discriminant of the quadratic equation.

DISCRIMINANT AND ROOTS