Question

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

±3, ±i
±2, ±i
positive or negative square root of 2 comma ±i
positive or negative square root 3, ±i

Answer 1

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