Question

Help please :))

The solutions to a polynomial equation include x = 3 (double root), and x = 2-3i, and has a leading coefficient of (-5). Write the polynomial equation, of smallest degree, with these characteristics, in standard form.

Answer 1

• See below

Explanation:

The roots are:

• 3, 3, 2 - 3i, 2 + 3i (conjugate of 2 - 3i should be added) and the leading coefficient is - 5

The polynomial is:

• -5(x - 3)² (x - [2 - 3i]) (x - [2 + 3i]) =
• - 5(x² - 6x + 9) (x² - 4x + 13) =
• -5(x⁴ - 10x³ + 46x² - 114x + 117) =
• -5x⁴ + 50x³ - 230x² + 570x - 585