Question

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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

Answer 1

1, 2, and ±i√8

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.