Questions and Answers
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 = 0
Use 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.
Solve the equation $(x + 12)(4x - 7) = 0 using the zero-factor property.
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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
Solving Quadratic Equations
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