precalculus

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solve the equation in the complex number system

x^4+x^3+4x^2+10x-60=0

  • precalculus -

    try x = 2
    16+8+16 +20 - 60 = 0 sure enough x = 2 works
    so divide by (x-2)
    x^3 + 3 x^2 + 10 x + 30
    write as
    x^3+10 x +3(x^2 +10)
    x(x^2+10) + 3(x^2+10)
    (x+3)(x^2+10)
    so
    x = -3 is a root
    left with x^2 = -10
    x = +/- i sqrt(10)
    so
    2, -3, i sqrt 10 , -i sqrt 10

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