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?
Quadratic equation:
x^2 + 5x + 6 = 0
To solve this equation by factoring, we need to find two numbers that multiply to 6 (the constant term) and add up to 5 (the coefficient of the linear term). These two numbers are 2 and 3.
Therefore, the factored form of the equation is:
(x + 2)(x + 3) = 0
Setting each factor to zero, we have:
x + 2 = 0 or x + 3 = 0
Solving for x, we get:
x = -2 or x = -3
Therefore, the solutions to the equation x^2 + 5x + 6 = 0 are x = -2 and x = -3.
To determine which method to use when solving a quadratic equation, you can consider the form of the equation and choose the method that fits best. For example, if the equation is in standard form (ax^2 + bx + c = 0) and can be easily factored, then factoring would be the best method to use. If the equation cannot be factored easily, then you may want to try using the quadratic formula or completing the square. Additionally, if the equation is in vertex form (y = a(x-h)^2 + k), you could use graphing or completing the square to find the solutions. Ultimately, the method you choose should be based on the specific characteristics of the quadratic equation you are trying to solve.