Final answer:
The quadratic equation x² + 1.2x - 6.0 × 10⁻³ = 0 can be solved using the quadratic formula to find x = -0.00240 and x = 0.00139, where in real-life scenarios, the positive solution x = 0.00139 is generally considered.
Step-by-step explanation:
To solve the quadratic equation x² + 1.2x - 6.0 × 10⁻³ = 0 using the quadratic formula, we first identify the coefficients a, b, and c. In this equation, a = 1, b = 1.2, and c = -6.0 × 10⁻³. The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a).
Substituting the coefficients into the formula gives us:
x = (-(1.2) ± √((1.2)² - 4 × 1 × (-6.0 × 10⁻³))) / (2 × 1)
Simplifying inside the square root gives:
x = (-1.2 ± √(1.44 + 24 × 10⁻³)) / 2
After calculating the discriminant and solving for x, we find that the solutions, rounded to five decimal places are x = -0.00240 and x = 0.00139. Since a negative time is not possible in real-life scenarios, we often consider the positive solution to be the more realistic one, so x = 0.00139 in such contexts.