What are the solutions of the equation x⁴ + 3x² + 2 = 0

An equation which has a degree equal to 4 is known as a biquadratic equation.

Answer: The solution for the equation x⁴ + 3x² + 2 = 0 is x = i,−i, i√2, −i√2.

Conversion of an even higher degree polynomial to a lower degree polynomial will help us to solve the given question.

Explanation:

Given: x⁴ + 3x² + 2 = 0

Substitute x²  = u into the given equation to make the fourth degree equation into a simple quadratic one.

New equation formed will be u² + 3u + 2 = 0

Factorising the above equation, we get,

⇒ (u + 2)(u + 1) = 0

Thus, u = -1 or -2

Replacing u back with x²,

x² = -1

⇒ x = i or - i  (Since, √-1 = i)

or 

x² = -2 

⇒ x = i√2 or −i√2

Therefore, the solution for the equation is x = i,−i, i√2, −i√2.