Find all real fourth roots of 16. 2 and -2 4 and -4
1 answer:
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Answer:
x = 1 or x = ± i
Step-by-step explanation:
Note the sum of the coefficients
1 - 1 + 1 - 1 = 0
This indicates that x = 1 is a root, thus (x - 1) is a factor
Using long division or synthetic division, then
x³ - x² + x - 1 = (x - 1)(x² + 1), thus
(x - 1)(x² + 1) = 0
Equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x² + 1 = 0 ⇒ x² = - 1 ⇒ x = ± = ± i