Question

Write a polynomial equation of degree 4 that has the following roots: -1 repeated three times and 4

Answer 1

9514 1404 393

Answer:

0 = x⁴ -x³ -9x² -11x -4

Explanation:

Each root r contributes a factor of (x-r). The factored form of the polynomial of interest is ...

0 = (x +1)³(x -4)

0 = (x³ +3x² +3x +1)(x -4)

0 = x⁴ -x³ -9x² -11x -4