Question

What are the roots of the equation 3x^2-4x+4=0?

Answer 1

`x=(2(1\pm i√(2) ))/(3)`

General Formulas and Concepts:

Pre-Alg

• Order of Operations: BPEMDAS

Alg I

• Standard Form: ax² + bx + c = 0
• Quadratic Formula:
  `x=(-b\pm√(b^2-4ac) )/(2a)`

• √-1 is imaginary number i

Explanation:

Step 1: Define

3x² - 4x + 4 = 0

a = 3

b = -4

c = 4

Step 2: Find roots

1. Substitute:
   `x=(-(-4)\pm√((-4)^2-4(3)(4)) )/(2(3))`
2. Simplify:
   `x=(4\pm√((-4)^2-4(3)(4)) )/(2(3))`
3. Evaluate:
   `x=(4\pm√(16-4(3)(4)) )/(2(3))`
4. Multiply:
   `x=(4\pm√(16-48) )/(6)`
5. Subtract:
   `x=(4\pm√(-32) )/(6)`
6. Factor:
   `x=(4\pm√(-1) √(32) )/(6)`
7. Simplify:
   `x=(4\pm4i√(2) )/(6)`
8. Factor:
   `x=(4(1\pm i√(2) ))/(6)`
9. Simplify:
   `x=(2(1\pm i√(2) ))/(3)`