# Solve The Quadratic Equation By Zero Product Property Worksheet

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To solve a quadratic equation using the zero product property, you set each factor involving the variable equal to zero. This method relies on the principle that if the product of two factors equals zero, then at least one of the factors must be zero. By solving each resulting linear equation, you find the values of the variable that satisfy the original quadratic equation.

Algebra 2

## How Will This Worksheet on “Solve the Quadratic Equation by Zero Product Property” Benefit Your Student's Learning?

• Reinforces factoring skills and deepens understanding of quadratic equations.
• Strengthens problem-solving abilities by providing structured practice.
• Improves comprehension of factors and solutions, essential for advanced math.
• Promotes interactive learning and engages students in active problem-solving.
• Supports self-paced learning, allowing students to master concepts at their own pace.

## How to Solve the Quadratic Equation by Zero Product Property?

• Ensure the quadratic equation is in the form ax^2 + bx + c = 0.
• Factor the quadratic expression on the left-hand side into two binomial expressions. This step might require finding two numbers that multiply to ac (the product of the coefficient of x^2 and the constant term) and add to b (the coefficient of x).
• Set each factor equal to zero. The zero product property states that if (x−p)(x−q)=0, then x-p=0 or x-q=0.
• Solve each equation separately to find the values of x.

## Solved Example

Q. Solve for $t$.$\newline$$(t + 9)(t - 7) = 0$$\newline$Write your answers as integers or as proper or improper fractions in simplest form.$\newline$$t =$ _____ or $t =$ _____
Solution:
1. Identify Property: Identify the property to use in solving the given equation.$\newline$Property: Zero product property, which states that if the product of two factors is $0$, then at least one of the factors must be $0$.
2. Apply Zero Product Property: Apply the zero product property to the equation $(t + 9)(t - 7) = 0$. Set each factor equal to zero: $t + 9 = 0$ and $t - 7 = 0$.
3. Solve First Equation: Solve the first equation $t + 9 = 0$.$\newline$Subtract $9$ from both sides to isolate $t$.$\newline$$t + 9 - 9 = 0 - 9$$\newline$$t = -9$
4. Solve Second Equation: Solve the second equation $t - 7 = 0$. Add $7$ to both sides to isolate $t$.$\newline$$t - 7 + 7 = 0 + 7$ $\newline$$t = 7$

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