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Algebra · Polynomial-Equations

Solve x^3 - 2 = 0

x^{3} - 2 = 0

Step by step

  1. x^{3} - 2 = 0

    Start from the equation as given.

  2. x^{3} - 2 = 0

    The polynomial has degree 3 and no rational factors; the roots come from the general solution.

  3. x = \sqrt[3]{2} \approx 1.2599 ,\; x = - \frac{\sqrt[3]{2}}{2} - \frac{\sqrt[3]{2} \sqrt{3} i}{2} ,\; x = - \frac{\sqrt[3]{2}}{2} + \frac{\sqrt[3]{2} \sqrt{3} i}{2}

    All 3 roots.

  4. x \approx 1.25992012 ,\; x \approx -0.62996006 - 1.09112358 i ,\; x \approx -0.62996006 + 1.09112358 i

    The exact forms are unwieldy (Cardano-style radicals); here they are numerically.

Reveal the answer
x \approx 1.25992012 ,\; x \approx -0.62996006 - 1.09112358 i ,\; x \approx -0.62996006 + 1.09112358 i