Question

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

3x² – 32x + 12 = 0

Answer 1

Given: 3x² – 32x + 12 = 0

Step-wise calculation:

1. Identify coefficients: a = 3, b = –32, c = 12.

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

3. Compute the discriminant:

D = (–32)² – 4 × 3 × 12 

= 1024 – 144

= 880

Since D > 0, the equation has two distinct real roots.

4. `sqrt(D) = sqrt(880)`

= `4sqrt(55)`

= 29.66479395

5. `x = (32 ± 29.66479395)/6`

`x_1 = (32 + 29.66479395)/6`

= `61.66479395/6`

= 10.27746566

= 10.28   ...(To 2 d.p.)

`x_2 = (32 - 29.66479395)/6`

= `2.33520605/6`

= 0.38920101

= 0.39   ...(To 2 d.p.)

x = 10.28 or x = 0.39.