Question

Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a brief evaluation of your work.

Activity
In this activity, you will solve quadratic equations using different methods. Make sure to use the method that you are asked for in each part.

Question 1
Solve the two equations in the table by factoring. Then enter those factors and the solutions in the table.

Equation Factors Solutions
x² +10 = 0 _____ _____

Answer 1

The equation x² +10 = 0 does not have real solutions by factoring because it cannot be factored with integers. For t² + 10t - 2000 = 0, by applying the quadratic formula, we find two possible solutions, 40 and -50.

Step-by-step explanation:

To solve the quadratic equation x² +10 = 0 by factoring, we first need to rearrange it into a form that can be factored. However, this equation cannot be factored using integers because there are no two numbers that multiply to give 10 and add to give 0. Therefore, the solutions to this equation are not real numbers.

In the case of t² + 10t - 2000 = 0, we can apply the quadratic formula to find the solutions. The quadratic formula is given by t = (-b ± √(b² - 4ac))/(2a). Plugging in the values from our equation where a=1, b=10, and c=-2000, we do the following steps:

1. Calculate the discriminant: b² - 4ac = 10² - 4(1)(-2000) = 100 + 8000 = 8100.
2. Calculate the square root of the discriminant: √8100 = 90.
3. Apply the quadratic formula:
   t = (-10 ± 90)/2.
4. Find the two possible solutions for t:
   t could be (-10 + 90)/2 = 40 or (-10 - 90)/2 = -50.