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?c
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1. Quadratic equation: x^2 + 5x + 6 = 0
To solve this equation by factoring, we need to find two numbers that multiply to 6 and add up to 5. The numbers are 2 and 3.
Therefore, the factored form of the equation is (x + 2)(x + 3) = 0
Setting each factor to zero, we get x + 2 = 0 and x + 3 = 0
Solving for x, we get x = -2 and 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 when solving a quadratic equation, it is important to consider the form of the equation and the techniques you have learned to solve equations.
- If the quadratic equation can be factored easily, factoring would be the most efficient method to use.
- If the quadratic equation is in the form ax^2 + bx + c = 0 and can be factored, factoring would be the best method to use.
- If the quadratic equation cannot be factored or if it is difficult to factor, using the quadratic formula or completing the square would be better options.
- If the quadratic equation is in a special form (perfect square trinomial or the difference of squares), using the appropriate method for that form would be the most effective way to solve the equation.
Ultimately, the method to use when solving a quadratic equation depends on the form of the equation and the techniques that will lead to the most efficient and accurate solution.