Its equally distant from the endpoints of the segment to find the center of the following rotation
Answer:
-10,10
Step-by-step explanation:
The given quadratic equation is
![k {x}^{2} + 20x + k = 0](https://tex.z-dn.net/?f=k%20%7Bx%7D%5E%7B2%7D%20%20%2B%2020x%20%2B%20k%20%3D%200)
The discriminant of this equation is given by;
![D = {b}^{2} - 4ac](https://tex.z-dn.net/?f=D%20%3D%20%20%7Bb%7D%5E%7B2%7D%20%20-%204ac)
where a=k, b=20, c=k
For rational solutions, the discriminant must be zero.
![{20}^{2} - 4 \times k \times k = 0](https://tex.z-dn.net/?f=%20%7B20%7D%5E%7B2%7D%20%20-%204%20%5Ctimes%20k%20%5Ctimes%20k%20%3D%200)
Simplify to get:
![400 - 4 {k}^{2} = 0](https://tex.z-dn.net/?f=400%20-%204%20%20%7Bk%7D%5E%7B2%7D%20%20%3D%200)
This implies that:
![400 = 4 {k}^{2}](https://tex.z-dn.net/?f=400%20%20%3D%204%20%20%7Bk%7D%5E%7B2%7D%20)
![100 = {k}^{2}](https://tex.z-dn.net/?f=100%20%3D%20%20%7Bk%7D%5E%7B2%7D%20)
Take square root to get:
![k = \pm\sqrt{100}](https://tex.z-dn.net/?f=k%20%3D%20%20%20%5Cpm%5Csqrt%7B100%7D%20)
![k = \pm10](https://tex.z-dn.net/?f=k%20%3D%20%20%5Cpm10)
![k = - 10 \: or \: k = 10](https://tex.z-dn.net/?f=k%20%3D%20%20-%2010%20%5C%3A%20or%20%5C%3A%20k%20%3D%2010)
Answer:
A
Step-by-step explanation:
look where the plot is Set 1 is at 8 and Set 2 is at 10. obviously 10 is greater than 8