Question

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

Answer 1

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
x² + 1 = 0
x² = -1 ⇒ no rational roots


The equation has no rational roots