Answer:

1, -2, 3, -4

Solutions:

Find the zeros of the polynomial equation x⁴ + 2x³ - 13x² -14x + 24 = 0.

x⁴ + 2x³ - 13x² - 14x + 24 = 0

x = 1

(1)⁴ + 2(1)³ - 13(1)² - 14(1) + 24 = 0

1 + 2 -13 -14 + 24 = 0

27 - 27 = 0

0 = 0

Then, 1 is a zero of the polynomial equation.

x = -2

(-2)⁴ + 2(-2)³ - 13(-2)² - 14(-2) + 24 = 0

16 + 2(-8) - 13(4) + 28 + 24 = 0

16 - 16 - 52 + 28 + 24 = 0

16 + 28 + 24 - 16 - 52 = 0

68 - 68 = 0

0 = 0

Then, -2 is also a zero of the polynomial equation.

x = 3

(3)⁴ + 2(3)³ - 13(3)² - 14(3) + 24 = 0

81 + 2(27) - 13(9) - 42 + 24 = 0

81 + 54 - 117 - 42 + 24 = 0

81 + 54 + 24 - 117 - 42 = 0

159 - 159 = 0

0 = 0

Then, 3 is also a zero of the polynomial equation.

x = -4

(-4)⁴ + 2(-4)³ - 13(-4)² - 14(-4) + 24 = 0

256 + 2(-64) - 13(16) + 56 + 24 = 0

256 - 128 - 208 + 56 + 24 = 0

256 + 56 + 24 - 208 - 128 = 0

336 - 336 = 0

0 = 0

Then, -4 is also a zero of the polynomial equation.

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