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Section 6.6 Solving Equations Using the Zero Product Rule
Introductory Algebra, Miller/O’Neill/Hyde
Andrea Hendricks
I. Overview
A. Sections 6.1 – 6.5 presented several factoring methods. We will apply these
methods to solving equations.
B. You will learn how to
1) Define a quadratic equation
2) Solve Equations Using the Zero Product Rule
3) Solve Applications of Quadratic Equations
4) Use the Pythagorean Theorem
II. Define a Quadratic Equation
A. Review
1) In Chapter 2, we learned how to solve linear equations in one variable.
2) Linear equations (ax + b = 0, a ≠ 0) are also called first-degree equations
because the highest degree of all its terms is 1.
3) Linear equations in one variable have one unique solution (unless they are a
contradiction or identity).
B. Quadratic Equations
1) A second-degree equation in one variable is called a quadratic equation. The
highest degree of all its terms is 2.
2) A quadratic equation is an equation that can be written in the form
ax 2  bx  c  0, a  0 and a, b, and c are real numbers.
3) We will learn that quadratic equations have two solutions, i.e. the degree of the
equation determines the number of solutions to the equation.
III. Solve Equations Using the Zero Product Rule
A. Zero Product Rule
1) A property of the real numbers will allow us to solve some quadratic equations.
2) The Zero Product Rule states that if the product of two factors is zero, then one
or both of its factors is zero.
3) If ab = 0, then a = 0 or b = 0.
B. Solve Quadratic Equations Using the Zero Product Rule
1) Write the equation in the form: ax 2  bx  c  0 .
2) Factor the equation completely using techniques from sections 6.1 – 6.5.
3) Set each factor equal to zero and solve the resulting equations.
4) Check by substitution into the original equation.
C. Solve Higher Degree Polynomial Equations
1) A higher degree polynomial equation has a degree greater than 2.
2) The degree will determine the number of solutions.
3) To solve, apply the process stated above.
IV. Applications of Quadratic Equations
A. Geometry Application
 Area of a rectangle (A = lw)
 Area of a triangle (A = ½bh)
B. Consecutive Integers (Section 2.4)
1) Consecutive integers: x, x+1, x+2, …
2) Consecutive odd integers: x, x+2, x+4, …
3) Consecutive even integers: x + x+2, x+4, …
C. Height models
D. Pythagorean Theorem
1) Provide formula, diagram, and terminology (legs, hypotenuse)
a 2  b 2  c 2 , where a and b are the legs and c is the hypotenuse
2) Find length of the missing side of the right triangle.
3) Real-life situations that make a right triangle application
 ladder leaning against a building
 distance between two objects
V. Summary – You should be able to
A. Solve quadratic equations using the Zero Product Rule.
B. Solve higher degree equations using the Zero Product Rule
C. Solve applications of quadratic equations.