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Test your understanding of solving quadratic equations using the zero-factor property with this quiz. Practice solving quadratic equations and other equations using key terms such as quadratic equation, standard form, and double root.

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@LavishCourage

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### Write the standard form of a quadratic equation.

The standard form of a quadratic equation is $ax^2 + bx + c = 0$, where $a$, $b$, and $c$ are constants with $a \neq 0$.

### Is f(x) = 2x +3 a quadratic equation? Explain why or why not.

No, because it is a linear equation.

### The zero-factor property states that If (a)(b) = 0 then a = 0 or b = 0Use the same property to solve (x+9)(5x-6)=0

Using the zero-factor property, the solutions are $x + 9 = 0$ and $5x - 6 = 0$, which give $x = -9$ and $x = \frac{6}{5}$ respectively.

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## Study Notes

### Solving Quadratic Equations Using the Zero-Factor Property

#### Learning Objectives

• Solve quadratic equations using the zero-factor property
• Solve other equations using the zero-factor property

### Important Terms

• Standard Form: The form of a quadratic equation written as ax^2 + bx + c = 0
• Double Solution: Two identical factors leading to the same solution
• Quadratic Equation: An equation that can be written in the form ax^2 + bx + c = 0, with a ≠ 0

#### Example: (x + 9)(5x - 6) = 0

• Apply the zero-factor property: x + 9 = 0 or 5x - 6 = 0
• Solve for x: x = -9 or x = 6/5

#### Example: (x + 12)(4x - 7) = 0

• Apply the zero-factor property: x + 12 = 0 or 4x - 7 = 0
• Solve for x: x = -12 or x = 7/4

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