Question

Find all the zeros of each function.

f(x)= x⁴-3x²- 4

Answer 1

x = ± 2 , x = ± i

Explanation:

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

`x^(4)` - 3x² - 4 = 0

substitute u = x² , then

u² - 3u - 4 = 0 ← in standard form

(u - 4)(u + 1) = 0 ← in factored form

equate each factor to zero and solve for u

u - 4 = 0 ⇒ u = 4

u + 1 = 0 ⇒ u = - 1

use the substitution to change back to variable x

x² = 4 ( take square root of both sides )

x = ±
`√(4)` = ± 2

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

x = ±
`√(-1)` = ± i

zeros are x = ± 2 , x = ± i