1. Write a quadratic equation that can be solved by factoring. Solve your equation and show and explain all your work.
2. In this unit you have learned about several different ways to solve quadratic equations. How do you determine which method to use when you’re trying to solve a quadratic equation?
1. Quadratic equation: x^2 + 5x + 6 = 0
To solve by factoring:
1. Find two numbers that multiply to 6 (the constant term) and add up to 5 (the coefficient of x). These numbers are 2 and 3.
2. Rewrite the middle term with these numbers: x^2 + 2x + 3x + 6 = 0
3. Factor by grouping: x(x + 2) + 3(x + 2) = 0
4. Factor out the common factor: (x + 2)(x + 3) = 0
5. Set each factor to zero and solve for x:
x + 2 = 0 or x + 3 = 0
x = -2 or x = -3
Therefore, the solutions to the quadratic equation x^2 + 5x + 6 = 0 are x = -2 and x = -3.
2. When determining which method to use to solve a quadratic equation, consider factors such as the coefficients of the terms, the type of roots, the accessibility of tools like a calculator or software, and personal preferences or familiarity with the methods. Some methods include factoring, completing the square, using the quadratic formula, and graphing to find the roots of a quadratic equation. Factoring may be preferred for relatively simple equations with integer solutions, while the quadratic formula is useful for any type of quadratic equation. Completing the square can be helpful when wanting to rewrite a quadratic equation in vertex form. Ultimately, the choice of method will depend on the specific equation and the resources available.