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 + 3x - 10 = 0
To solve this equation by factoring, we need to find two numbers that multiply to -10 and add up to 3. The numbers that satisfy this condition are 5 and -2. Rewrite the equation:
(x + 5)(x - 2) = 0
Setting each factor equal to zero:
x + 5 = 0 or x - 2 = 0
x = -5 or x = 2
Therefore, the solutions to the quadratic equation x^2 + 3x - 10 = 0 are x = -5 and x = 2.
When determining which method to use to solve a quadratic equation, it is important to consider the form of the equation and the available methods. Factoring is most suitable for simple quadratics with integer coefficients, while completing the square or using the quadratic formula may be better for more complex or non-factorable equations. It is also useful to consider how comfortable you are with each method and choose the one that you feel most confident in using. Ultimately, the goal is to efficiently and accurately find the solutions to the quadratic equation.