Which are the solutions of the equation x^4 - 5x^2 - 36 = 0

x = ± 3, x = ± 2i

Step-by-step explanation:

Given

- 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 = ± = ± 3 ← real roots

u = - 4 ⇒ x² = - 4 ⇒ x = ± = ± 2i ← imaginary roots

step-by-step explanation:

1

his first public project he is asked to create a small scale drawing. the garden is a right triangle with base 25m and height 30m. are you trying to solve for the last side/hypotenuse? the irrational form of the answer would be 5\sqrt{61}