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Is it possible for a degree-4 polynomial P(x) to have only complex (no real) roots

  • algebra -

    work backwards from 4 imaginary roots (remember they come in complex conjugate pairs)
    (x-i)(x+i)(x-2i)(x+2i) = 0
    (x^2+1)(x^2+4)= 0
    x^4 + 5 x^2 + 4 = 0

  • algebra -

    Is it possible for a degree-4 polynomial P(x) to have only complex (no real) roots?

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