Question

Find the zeroes of the polynomial function f(x)=x^4-5x^3+11x^2-25x+30.

Answer 1

Step-by-step explanation:

x⁴ − 5x³ + 11x² − 25x + 30

x⁴ − 5x³ + 6x² + 5x² − 25x + 30

x² (x² − 5x + 6) + 5 (x² − 5x + 6)

(x² + 5) (x² − 5x + 6)

(x² + 5) (x − 2) (x −3)

The zeros are 2, 3, and ±√5i.