Question

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

4x² – 7x + 2 = 0

Answer 1

Given: 4x² – 7x + 2 = 0

Step-wise calculation:

1. Compare with ax² + bx + c = 0: a = 4, b = –7, c = 2.

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

3. Compute the discriminant:

D = (–7)² – 4 × 4 × 2 

= 49 – 32

= 17

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

4. Evaluate: `x = (7 ± sqrt(17))/8`

`sqrt(17) = 4.123105626`

`x_1 = (7 + 4.123105626)/8`

= 1.390388203

`x_2 = (7 - 4.123105626)/8`

= 0.359611797

Correct to 2 decimal places: x = 1.39 or x = 0.36.