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.
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)
x2 = -2
⇒ x = i√2 or −i√2