a) 0 = x⁴ - 81
0 = (x² - 9)(x² + 9)
0 = (x - 3)(x + 3)(x² + 9)
0 = x - 3 , 0 = x + 3 , 0 = x² + 9
x = 3 , x = -3 , x² = -9 → x = √-9 → x = +/- 3i
Answer: real roots 3, 3 ; complex roots 3i, -3i
b) 0 = x⁴ + 10x² + 25
0 = (x² + 5)²
0 = x² + 5
x² = -5 → x = +/-√-5 → x = +/- i√5
Answer: no real roots ; complex roots i√5, -i√5
c) 0 = x⁴ - x² - 6
0 = (x² - 3)(x² + 2)
0 = x² - 3 0 = x² + 2
x² = 3 → x = +/-√3 x² = -2 → x = +/-√-2 → x = +/-i√2
Answer: real roots √3, -√3; complex roots i√2, -i√2