The solutions for the quadratic equation 9x² - 6x + 5 = 0 are A. 2 complex roots
To determine the the type of roots the quadratic equation 9x² - 6x + 5 = 0, we use the quadratic formula to find the roots.
So, for a quadratic equation ax + bx + c = 0, the roots are
![x = \frac{-b +/- \sqrt{b^{2} - 4ac} }{2a}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-b%20%2B%2F-%20%5Csqrt%7Bb%5E%7B2%7D%20-%204ac%7D%20%7D%7B2a%7D)
With a = 9, b = -6 and c = 5, the roots of our equation are
![x = \frac{-(-6) +/- \sqrt{(-6)^{2} - 4 X 9 X 5} }{2 X 9} \\x = \frac{6 +/- \sqrt{36 - 180} }{18} \\x = \frac{6 +/- \sqrt{-144} }{18} \\x = \frac{6 +/- \sqrt{-12} }{18}\\x = \frac{6}{18} +/- i\frac{12}{18} \\x = \frac{1}{3} +/- i\frac{2}{3} \\x = \frac{1 + 2i}{3} or \frac{1 - 2i}{3}](https://tex.z-dn.net/?f=x%20%3D%20%5Cfrac%7B-%28-6%29%20%2B%2F-%20%5Csqrt%7B%28-6%29%5E%7B2%7D%20-%204%20X%209%20X%205%7D%20%7D%7B2%20X%209%7D%20%5C%5Cx%20%3D%20%5Cfrac%7B6%20%2B%2F-%20%5Csqrt%7B36%20-%20180%7D%20%7D%7B18%7D%20%5C%5Cx%20%3D%20%5Cfrac%7B6%20%2B%2F-%20%5Csqrt%7B-144%7D%20%7D%7B18%7D%20%5C%5Cx%20%3D%20%5Cfrac%7B6%20%2B%2F-%20%5Csqrt%7B-12%7D%20%7D%7B18%7D%5C%5Cx%20%3D%20%5Cfrac%7B6%7D%7B18%7D%20%2B%2F-%20i%5Cfrac%7B12%7D%7B18%7D%20%5C%5Cx%20%3D%20%5Cfrac%7B1%7D%7B3%7D%20%2B%2F-%20i%5Cfrac%7B2%7D%7B3%7D%20%5C%5Cx%20%3D%20%5Cfrac%7B1%20%2B%202i%7D%7B3%7D%20%20or%20%5Cfrac%7B1%20-%202i%7D%7B3%7D)
Since the roots of the equation are (1 + 2i)/3 and (1 - 2i)/3, there are 2 complex roots.
So, the solutions for the quadratic equation 9x² - 6x + 5 = 0 are A. 2 complex roots
Learn more about quadratic equations here:
brainly.com/question/18117039
Answer:
No solutions for n
Step-by-step explanation:
Distribute the 4 to the -8 and the 2n
-4 + 4*-8 + 4*2n = -37 + 8n
Multiply
-4 - 32 + 8n = -37 + 8n
Subtract 8n on both sides
-4 - 32 = -37
Subtract on the left
-36 = -37
No solutions because -36 does not equal -37
Answer:
There are two orders in which we can do the steps:
1. GAFDC
2. GABEC
Step-by-step explanation:
![4x-8=5x-2(x+2)](https://tex.z-dn.net/?f=4x-8%3D5x-2%28x%2B2%29)
Step 1 :G Using distributive property to remove parenthesis:
![4x-8=5x+(-2\times x-2\times2)](https://tex.z-dn.net/?f=4x-8%3D5x%2B%28-2%5Ctimes%20x-2%5Ctimes2%29)
![4x-8=5x-2x-4](https://tex.z-dn.net/?f=4x-8%3D5x-2x-4)
Step 2:A Collect like terms:
![4x-8=3x-4](https://tex.z-dn.net/?f=4x-8%3D3x-4)
Step 3: F Add 8 to both sides:
![4x-8+8=3x-4+8](https://tex.z-dn.net/?f=4x-8%2B8%3D3x-4%2B8)
![4x=3x+4](https://tex.z-dn.net/?f=4x%3D3x%2B4)
Step 4: D Subtract
from both sides:
![4x-3x=3x+4-3x](https://tex.z-dn.net/?f=4x-3x%3D3x%2B4-3x)
![x=4](https://tex.z-dn.net/?f=x%3D4)
Solution:C
![x=4](https://tex.z-dn.net/?f=x%3D4)
Or
![4x-8=5x-2(x+2)](https://tex.z-dn.net/?f=4x-8%3D5x-2%28x%2B2%29)
Step 1 :G Using distributive property to remove parenthesis:
![4x-8=5x+(-2\times x-2\times2)](https://tex.z-dn.net/?f=4x-8%3D5x%2B%28-2%5Ctimes%20x-2%5Ctimes2%29)
![4x-8=5x-2x-4](https://tex.z-dn.net/?f=4x-8%3D5x-2x-4)
Step 2:A Collect like terms:
![4x-8=3x-4](https://tex.z-dn.net/?f=4x-8%3D3x-4)
Step 4: B Subtract
from both sides:
![4x-8-3x=3x-4-3x](https://tex.z-dn.net/?f=4x-8-3x%3D3x-4-3x)
![x-8=-4](https://tex.z-dn.net/?f=x-8%3D-4)
Step 3: E Add 8 to both sides:
![x-8+8=-4+8](https://tex.z-dn.net/?f=x-8%2B8%3D-4%2B8)
![x=4](https://tex.z-dn.net/?f=x%3D4)
Solution:C
![x=4](https://tex.z-dn.net/?f=x%3D4)
There are two orders in which we can do the steps:
1. GAFDC
2. GABEC
One way:
5.375+3.2 = 8.575, or 8 23/40. LCD is 40.
Answer:
The Answer is B.
Step-by-step explanation: