Question

If α and β are zeroes of a polynomial x² + 6x + 9, then form a polynomial whose zeroes are -α and -β

Answer 1

x² - 6x + 9

General Formulas and Concepts:

Algebra I

• Factoring
• Expand by FOIL (First Outside Inside Last)

Explanation:

Step 1: Define

x² + 6x + 9

Step 2: Find Roots α and β

1. Factor quadratic: (x + 3)²
2. Find roots: α = -3, β = -3

Step 3: Solve

1. Apply negatives: -α = -(-3), -β = -(-3)
2. Multiply: -α = 3, -β = 3
3. Write binomial factor: (x - 3)²
4. Expand [FOIL]: x² - 6x + 9