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What are the roots of the polynomial equation?

You can use any method you would like to solve.

0=x^4-3x^3+10x^2-24+16

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.