The equation has two real and equal roots for ![k = \frac{5}{6}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B5%7D%7B6%7D)
In this question, we use the concept of the solution of a quadratic equation to solve it, considering that a quadratic equation in the format:
![ax^2 + bx + c = 0](https://tex.z-dn.net/?f=ax%5E2%20%2B%20bx%20%2B%20c%20%3D%200)
has two equal solutions if
is 0.
------------------------------------
In this question:
The equation is:
![(2k+1)x^2 + 2x = 10x - 6](https://tex.z-dn.net/?f=%282k%2B1%29x%5E2%20%2B%202x%20%3D%2010x%20-%206)
Placing in the correct format:
![(2k+1)x^2 + 2x - 10x + 6 = 0](https://tex.z-dn.net/?f=%282k%2B1%29x%5E2%20%2B%202x%20-%2010x%20%2B%206%20%3D%200)
![(2k+1)x^2 - 8x + 6 = 0](https://tex.z-dn.net/?f=%282k%2B1%29x%5E2%20-%208x%20%2B%206%20%3D%200)
Thus, the coefficients are: ![a = 2k + 1, b = -8, c = 6](https://tex.z-dn.net/?f=a%20%3D%202k%20%2B%201%2C%20b%20%3D%20-8%2C%20c%20%3D%206)
------------------------------------
Delta:
We want it to be positive, so:
![\Delta = b^2 - 4ac](https://tex.z-dn.net/?f=%5CDelta%20%3D%20b%5E2%20-%204ac)
![\Delta = 0](https://tex.z-dn.net/?f=%5CDelta%20%3D%200)
![b^2 - 4ac = 0](https://tex.z-dn.net/?f=b%5E2%20-%204ac%20%3D%200)
![(-8)^2 - 4(2k+1)(6) = 0](https://tex.z-dn.net/?f=%28-8%29%5E2%20-%204%282k%2B1%29%286%29%20%3D%200)
![64 - 48k - 24 = 0](https://tex.z-dn.net/?f=64%20-%2048k%20-%2024%20%3D%200)
![-48k + 40 = 0](https://tex.z-dn.net/?f=-48k%20%2B%2040%20%3D%200)
![-48k = -40](https://tex.z-dn.net/?f=-48k%20%3D%20-40)
![48k = 40](https://tex.z-dn.net/?f=48k%20%3D%2040)
![k = \frac{40}{48}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B40%7D%7B48%7D)
![k = \frac{5}{6}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B5%7D%7B6%7D)
The equation has two real and equal roots for ![k = \frac{5}{6}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B5%7D%7B6%7D)
A similar question is found at brainly.com/question/12144265
Answer:
a = 240
Step-by-step explanation:
To solve for a, divide 48 by 0.2:
0.2a = 48
a = 48 / 0.2 = 240
Answer:
undefined
Step-by-step explanation:
when there is a vertical line, the slope is undefined and when it is a horizontal line, it is 0