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?
For your original discussion post, you only need to respond to #1 and #2.
3. View posts from your classmates and choose one to respond to. Look at the equation that your classmate created and then solve it using a method other than factoring. Show all your work. Did you get the same answer? Do you agree with your classmate’s response about determining which method to use when solving a quadratic equation? Why or why not?
4. View responses and comment on the work of another classmate. You may correct any errors that you find, show another way to solve the problem, or provide constructive feedback on the work.
1. Quadratic equation: 2x^2 + 5x - 3 = 0
To solve this by factoring, we need to find two numbers that multiply to -6 (the product of the coefficients of the x^2 term and the constant term) and add up to 5 (the coefficient of the x term).
The factors of -6 are -6 and 1, and -2 and 3. Since we want the sum to be positive, we use -2 and 3.
Therefore, we can rewrite the equation as:
2x^2 - 2x + 8x - 3 = 0
2x(x - 1) + 3(x - 1) = 0
(2x + 3)(x - 1) = 0
Setting each factor to zero gives us:
2x + 3 = 0 or x - 1 = 0
2x = -3 x = 1
x = -3/2
So, the solution to the equation is x = -3/2 and x = 1.
2. When determining which method to use when solving a quadratic equation, it is important to consider the specific form of the equation and the skills and knowledge you have to solve it. Factoring is usually the quickest and most efficient method if the equation is easily factorable. Otherwise, methods such as completing the square or using the quadratic formula can be used depending on the complexity of the equation.
3. Response to classmate:
Equation provided: 3x^2 - 9x + 6 = 0
To solve this equation using the quadratic formula:
a = 3, b = -9, c = 6
x = (-(-9) ± √((-9)^2 - 4*3*6)) / 2*3
x = (9 ± √(81 - 72)) / 6
x = (9 ± √9) / 6
x = (9 ± 3) / 6
x = 12/6 or 6/6
x = 2 or 1
Therefore, the solutions to the equation are x = 2 and x = 1. In this case, I agree with your method of using the quadratic formula because the equation was not easily factorable.
4. Comment on classmate's work:
Your work on solving the quadratic equation using the quadratic formula is correct and well-explained. It's important to show all the steps clearly to demonstrate the process of solving the equation accurately. Keep up the good work!