Which are the solutions of the equation x^4 – 5x^2 – 36 = 0 Question Which are the solutions of the equation x^4 – 5x^2 – 36 = 0 in progress 0 Math Amara 1 month 2021-10-12T09:01:54+00:00 2021-10-12T09:01:54+00:00 2 Answers 0 views 0

## Answers ( )

Answer: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

4x-10x = 36

-6x = 36

X= -6