Question

Solve for x and give your answer correct to 2 decimal places:

2x² – 6x + 3 = 0

Answer 1

Given: 2x² – 6x + 3 = 0

Step-wise calculation:

1. Identify coefficients: a = 2, b = –6, c = 3.

2. Use the quadratic formula `x = (-b ± sqrt(b^2 - 4ac))/(2a)`.

3. Compute the discriminant: b² – 4ac

= (–6)² – 4 × 2 × 3 

= 36 – 24

= 12

4. `sqrt(12) = 2sqrt(3)`, 

So, `x = (6 ± sqrt(12))/4` 

= `(6 ± 2sqrt(3))/4` 

= `(3 ± sqrt(3))/2`

5. Numerical values `(sqrt(3) ≈ 1.7320508)`: 

`x_1 = (3 + 1.7320508)/2`

= 2.3660254

= 2.37   ...(To 2 d.p.) 

`x_2 = (3 - 1.7320508)/2`

= 0.6339746

= 0.63   ...(To 2 d.p.)

x = 2.37 or x = 0.63 correct to 2 decimal places.