Question

Write a polynomial of degree 3 whose only roots are x=2 and x=2/5. Is there another polynomial of degree 3 that has the same roots?

Answer 1

Explanation:

(x - 2)² (x - 2/5) = 0

5(x - 2)² (x - 2/5) = 0

(x - 2)² * 5(x - 2/5) = 0

(x - 2)² (5x - 2) = 0

(x² - 4x + 4)(5x - 2) = 0

5x³ - 20x² + 20x - 2x² + 8x - 8 = 0

5x³ - 22x² + 28x - 8 = 0

Another possible polynomial is

(x - 2) (x - 2/5)² = 0