Question

Find the roots of the following equation, if they exist, by applying the quadratic formula:

x² – 6x + 4 = 0

Answer 1

Given: x² – 6x + 4 = 0

Step-wise calculation:

1. Identify coefficients:

a = 1, b = –6, c = 4

2. Discriminant:

D = b² – 4ac

= (–6)² – 4(1)(4) 

= 36 – 16

= 20

3. Square root:

`sqrt(D) = sqrt(20)` 

= `2sqrt(5)`

4. Quadratic formula:

`x = (-b ± sqrt(D))/(2a)`

Using that formula,

`x = (6 ± 2sqrt(5))/2` 

= `3 ± sqrt(5)`

The roots are `x = 3 + sqrt(5)` and `x = 3 - sqrt(5)`.