How many rational roots does x4 + 3x2 + 2 = 0 have?

X⁴ + 3x² + 2 = 0

x⁴ + 2x² + x² + 2 = 0

x² (x² + 2) + (x² + 2) = 0

(x² + 2) * (x² + 1) = 0

x² + 2 = 0

x² = - 2 ⇒ no rational roots

or

x ² + 1 = 0

x² = - 1 ⇒ no rational roots

The equation has no rational roots