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Dafna1 [17]
2 years ago
15

What are the zeros of the function f(x) = x4 − x2 − 2?

Mathematics
1 answer:
goblinko [34]2 years ago
8 0

Answer:

x = ± \sqrt{2} , x = ± i

Step-by-step explanation:

f(x) = x^{4} - x² - 2

to find the zeros , equate f(x) to zero , that is

x^{4} - x² - 2 = 0

using the substitution u = x² , then

u² - u - 2 = 0 ← in standard form

(u - 2)(u + 1) = 0 ← in factored form

equate each factor to zero and solve for u

u - 2 = 0 ⇒ u = 2

u + 1 = 0 ⇒ u = - 1

convert u back into terms of x

x² = 2 ( take square root of both sides )

x = ± \sqrt{2}

x² = - 1 ( take square root of both sides )

x = ± \sqrt{-1} = ± i

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