What are the Solutions of the Equation x⁴ + 3x² + 2 = 0? Use "u" substitution to solve.

Solution:

Given: x⁴ + 3x² + 2 = 0

Consider u = x²

u² + 3u + 2 = 0

It can be written as

(u + 1)(u + 2) = 0 [factorizing the quadratic equation]

u = -1 and u = -2

So we get

x² = -1 and x² = -2

Here we get the complex roots.

x\(_1\) = √-1 = i

x\(_2\)  = -√-1 = -i

x\(_3\) = √-2 = i√2

x\(_4\)  = -√-2 = -i√2

Therefore, the solutions of the equation are x = i, -i, i√2, -i√2.

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What are the Solutions of the Equation x⁴ + 3x² + 2 = 0? Use "u" substitution to solve.

Summary:

The solutions of the equation x⁴ + 3x² + 2 = 0 are x = i, -i, i√2, -i√2.