Question

Task 2: The Quadratic FormulaThe process of completing the square, which is what you did in task 1, will work for any quadratic equation that has solutions. Using this technique, it is possible to create a formula that you can apply to any quadratic equation. In this task, you will derive and use the quadratic formula.⦁1 If the variables a, b, and c are all real numbers and a is not equal to 0, then apply the process of completing the square to solve the following general equation for x. Write your final answer as a single fraction. Show your work.Type your response here:⦁2 The result from part a is called the quadratic formula. Use the formula to solve the quadratic equation 5x2 – 3x − 12 = 0. Show your work.Type your response here:⦁3 Do you prefer the method of completing the square or using the quadratic formula? Why?Type your response here:

Answer 1

1. Supposing the equation is ax^2+bx+c

2.

5x^2 - 3x - 12 = 0

Apply the quadratic formula:

$\frac{-b\pm\sqrt[]{b^2-4\cdot a\cdot c}}{2\cdot a}$

ax^2 +bx+c=0

For the equation given:

a = 5

b= -3

c= -12

Replacing:

$\frac{-(-3)\pm\sqrt[]{(-3)^2-4\cdot5\cdot-12}}{2\cdot5}$$\frac{3\pm\sqrt[]{9+240}}{10}$$\frac{3\pm\sqrt[]{249}}{10}$$\frac{3+\sqrt[]{249}}{10}\text{ and }\frac{3-\sqrt[]{249}}{10}$

Solutions in decimals:

x = 1.878 , x = -1.278