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6 October, 12:54

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

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  1. 6 October, 13:22
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    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
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