Precalculus

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Solve the equation x^3 - 2x + 4 = 0.

==> I know the answer is -2, but I can't seem to remember how to solve these by hand without using a graphing calculator. Any help is greatly appreciated!! :)

  • Precalculus -

    Unless they factor, cubic equations cannot be easily solved "by hand"
    In this case, try subbing ±1 and ±2 into the equation to get a zero.
    You were right to find that x = -2 works
    so (x+2) must be a factor.
    Use long algebraic division or synthetic division to find the other factor to be (x^2 - 2x + 2)

    using the quadratic formula on
    x^2 - 2x + 2 = 0 gives me two complex roots, namely (1 ± i)/2

  • correction - Precalculus -

    the two complex roots should have been just
    1 ± i

  • Precalculus -

    Ohhh I see. Thanks Reiny this helped a lot!! :)

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