Final answer:
To find all zeros of the polynomial x² + 1.2 × 10⁻²x - 6.0 × 10⁻³, use the quadratic formula with a = 1, b = 1.2 × 10⁻², and c = – 6.0 × 10⁻³. Calculate the discriminant, apply the formula, and list the two zeros, rounded to four decimal places, as a comma-separated list.
Step-by-step explanation:
To find all the zeros of the polynomial x² + 1.2 × 10⁻²x - 6.0 × 10⁻³, we can use the quadratic formula, which is defined as x = –b ± √(b² – 4ac)/(2a) for a quadratic equation of the form ax² + bx + c = 0. For our equation:
• a = 1
• b = 1.2 × 10⁻²
• c = –6.0 × 10⁻³
Plugging these values into the quadratic formula, we get:
x = –(1.2 × 10⁻²) ± √((1.2 × 10⁻²)² – 4 × 1 × (–6.0 × 10⁻³))/(2 × 1)
Simplify and calculate this expression to find the two zeros, remembering to round to four decimal places as needed and maintaining proper units and significant figures. After calculating, list the two zeros separated by a comma.
For example, if the calculation gives us values of 0.1 and –0.05, you would enter "0.1, –0.05".
Important Steps to Consider
1. Enter the relevant data into a calculator or a computer
2. Rewrite the quadratic equation in the standard form if needed
3. Use the quadratic formula to calculate the zeros
4. Round your answer to four decimal places where appropriate
5. Check your answer to ensure it's reasonable and maintains the appropriate number of significant figures