Solve the following mathematical questions: Equation: x² - 7x + 3 = 0. Give your answer correct to two decimal places.

Given:

x² − 7x + 3 = 0

Here: a = 1 b = −7 c = 3

Quadratic formula:

x = [−b ± √(b² − 4ac)]/(2a)

= [7 ± √{(−7)² − 4(1)(3)}]/2

= [7 ± √37]/2

√37 ≈ 6.08276

Therefore:

x ≈ (7 + 6.08276)/2 = 6.54138

or

x ≈ (7 − 6.08276)/2 = 0.45862

Correct to two decimal places:

Answer:

x = 6.54 or 0.46.

The quadratic formula gives two real roots because the discriminant is 37. Rounding the calculated roots to two decimal places gives 6.54 and 0.46.