Answer:
1, 2, and ±i√8
Step-by-step explanation:
0 = x⁴ − 3x³ + 10x² − 24x + 16
Using grouping:
0 = x⁴ − 3x³ + 2x² + 8x² − 24x + 16
0 = x² (x² − 3x + 2) + 8 (x² − 3x + 2)
0 = (x² + 8) (x² − 3x + 2)
0 = (x² + 8) (x − 1) (x − 2)
The roots are 1, 2, and ±i√8.
