Solve a quadratic equation using the zero product property

Key Notes :

Understanding the Zero Product Property

  • The Zero Product Property states that if the product of two factors is zero, then at least one of the factors must be zero.
  • This property is used to solve quadratic equations that can be factored into the form (a + b)(c + d) = 0.

Steps to Solve Using the Zero Product Property

  1. Factor the Quadratic Equation: Express the quadratic equation in the form (a + b)(c + d) = 0.
  2. Set Each Factor Equal to Zero: Create two separate equations:
    • a + b = 0
    • c + d = 0
  3. Solve Each Equation: Solve each equation independently to find the values of x that make the factors zero.

Example

Solve: x² – 4x + 3 = 0

  • Step 1: Factor the equation: (x – 1)(x – 3) = 0
  • Step 2: Set each factor equal to zero:
    • x – 1 = 0
    • x – 3 = 0
  • Step 3: Solve each equation:
    • x = 1
    • x = 3

Key Points

  • The Zero Product Property is a powerful tool for solving quadratic equations that can be factored.
  • Factoring the quadratic equation is crucial for applying this method.
  • Setting each factor equal to zero creates two separate equations to solve.
  • The solutions to the equations represent the values of x that make the original quadratic equation true.

Learn with an example

Solve for r.

(r + 3)(r + 9) = 0


Write your answers as integers or as proper or improper fractions in simplest form.

r = ________ or r =________

According to the Zero Product Property, if (r + 3)(r + 9) = 0, then (r + 3) must be 0 or (r + 9) must be 0. Write two equations and solve for r.

r+3=0 or r+9=0

r=-3 r=-9

The solution is r = -3 or r = -9.

Solve for n.

n(n + 2) = 0


Write your answers as integers or as proper or improper fractions in simplest form.

n = ________ or n = ________

According to the Zero Product Property, if n(n + 2) = 0, then n must be 0 or (n + 2) must be 0. Write two equations and solve for n.

n=0 or n+2=0

n=-2

The solution is n = 0 or n = -2.

Solve for q.

(q + 4)(q − 8) = 0


Write your answers as integers or as proper or improper fractions in simplest form.

q =________or q = ________

According to the Zero Product Property, if (q + 4)(q − 8) = 0, then (q + 4) must be 0 or (q − 8) must be 0. Write two equations and solve for q.

q+4=0 or q-8=0

q=-4 q=-8

The solution is q = -4 or q = 8.

let’s practice!