Answer:
The roots are real and distinct.
Step-by-step explanation:
Given the following equation:
![x^{2} + kx - k -2 =0](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%2B%20kx%20-%20k%20-2%20%3D0)
In this problem, a = 1, b = k and c = -k - 2
The discriminant is b² - 4ac, and for the roots to be real and distinct, it must be at least or greater than 0.
We get,
(k)²- 4(1)(-k - 2) = 1 - 4(-k - 2)
= k² + 4k + 8
Let's check:
At k = -2,
![(-2)^{2} + 4(-2) + 8 = 4 - 8 + 8 = 4 ](https://tex.z-dn.net/?f=%28-2%29%5E%7B2%7D%20%2B%204%28-2%29%20%2B%208%20%3D%204%20-%208%20%2B%208%20%3D%204%0A%0A%0A)
At k = 0,
![(0)^2 + 4(0) + 8 = 8](https://tex.z-dn.net/?f=%280%29%5E2%20%2B%204%280%29%20%2B%208%20%3D%208%20)
At k = -100,
![(-100)^2 + 4(-100) + 8 = 10,000 - 400 + 8 = 9608](https://tex.z-dn.net/?f=%28-100%29%5E2%20%2B%204%28-100%29%20%2B%208%20%3D%2010%2C000%20-%20400%20%2B%208%20%3D%209608)
Therefore, we can conclude that for all values of k, the roots are real and distinct.
This has been a long way in answering this question, so it would be great if you could mark me as brainliest
Yes! It is a function.
actually y=x is a straight line passing through the origin on an XY Axis; with an inclination of 45 degrees to the positive X-Axis.
Answer:
Sabrina will train 21 miles next week for the race.
Step-by-step explanation:
2/3 of 4.2=2.8
%25 more of 2.8=3.5
3.5*6=21 miles
Answer:
5
Step-by-step explanation:
Answer:
CD
Step-by-step explanation:
For all sides except CD, you do not need the distance formula, since they are vertical or horizontal, meaning that you can find their length simply through subtraction. However, with side CD, since it is diagonal, you need to form a right triangle with to solve its length. Hope this helps!