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17 March, 02:41

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What are the roots of the polynomial equation?

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

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  1. 17 March, 02:52
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    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.
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