# What are the solutions of the equation x^{4 }+ 3x^{2 }+ 2 = 0

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

## Answer: The solution for the equation x^{4 }+ 3x^{2 }+ 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: x^{4 }+ 3x^{2 }+ 2 = 0

Substitute x^{2 } = u into the given equation to make the fourth degree equation into a simple quadratic one.

New equation formed will be u^{2} + 3u + 2 = 0

Factorising the above equation, we get,

⇒ (u + 2)(u + 1) = 0

Thus, u = -1 or -2

Replacing u back with x^{2},

x^{2} = -1

⇒ x = i or - i (Since, √-1 = i)

or

x^{2} = -2

⇒ x = i√2 or −i√2