Final answer:
To find the x-intercepts for the quadratic equation x² + 1.2 x 10⁻²x - 6.0 × 10⁻³ = 0, we use the quadratic formula with coefficients a=1, b=1.2 x 10⁻², and c=-6.0 x 10⁻³. After plugging these into the formula, we calculate and consider only the valid solutions for x.
Step-by-step explanation:
To solve a quadratic equation of the form ax² + bx + c = 0, we use the quadratic formula:
x = (-b ± √(b² - 4ac)) / (2a)
Let's solve the equation x² + 1.2 x 10⁻²x - 6.0 × 10⁻³ = 0 using the quadratic formula:
Identify the coefficients: here a = 1, b = 1.2 x 10⁻², and c = -6.0 x 10⁻³.
Plug the coefficients into the quadratic formula:
Calculate the discriminant: √(b² - 4ac).
Find the two possible solutions for x by solving the positive and negative versions separately.
If you obtain a negative value for x in a real-world context and it doesn't make sense (like a negative distance), then that value of x is not a valid solution.