Answer:
x = ± 3, x = ± 2i
Step-by-step explanation:
Given
[tex]x^{4}[/tex] - 5x² - 36 = 0
Use the substitution u = x² then the equation is
u² - 5u - 36 = 0 ← in standard form
(u - 9)(u + 4) = 0 ← in factored form
Equate each factor to zero and solve for u
u - 9 = 0 ⇒ u = 9
u + 4 = 0 ⇒ u = - 4
This indicates there will be 2 real roots and 2 complex roots
Change back to find values of x, that is
u = 9 ⇒ x² = 9 ⇒ x = ± [tex]\sqrt{9}[/tex] = ± 3 ← real roots
u = - 4 ⇒ x² = - 4 ⇒ x = ± [tex]\sqrt{-4}[/tex] = ± 2i ← imaginary roots
