(x+4)(x-5)=0 Standard Form

Jasonbradley

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Jun 16, 2024

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Solving Quadratic Equations: From Factored Form to Standard Form

This article focuses on understanding the relationship between factored form and standard form of a quadratic equation, specifically using the example: (x + 4)(x - 5) = 0.

Understanding Factored Form

The equation (x + 4)(x - 5) = 0 is presented in factored form. This form is useful for quickly finding the roots or solutions of the equation.

The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero.

Applying this to our equation:

• x + 4 = 0 or x - 5 = 0
• Solving for x in each case, we get:
  • x = -4
  • x = 5

Therefore, the roots of the equation (x + 4)(x - 5) = 0 are x = -4 and x = 5.

Converting to Standard Form

The standard form of a quadratic equation is ax² + bx + c = 0, where a, b, and c are constants and a ≠ 0.

To convert our factored form into standard form, we need to expand the product:

1. FOIL Method: We multiply each term in the first factor by each term in the second factor.
   • (x + 4)(x - 5) = x(x - 5) + 4(x - 5)
2. Simplify: We distribute and combine like terms.
   • x² - 5x + 4x - 20 = 0
3. Combine Like Terms:
   • x² - x - 20 = 0

Therefore, the standard form of the quadratic equation (x + 4)(x - 5) = 0 is x² - x - 20 = 0.

Conclusion

By understanding the relationship between factored form and standard form, we can efficiently solve quadratic equations. The factored form provides a direct path to finding the roots, while the standard form is essential for various mathematical operations and applications.