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Roots of $$$f{\left(x \right)} = x^{4} - 4 x^{3} + 9 x^{2} + 5 x + 14$$$

The calculator will try to find all roots of the polynomial $$$f{\left(x \right)} = x^{4} - 4 x^{3} + 9 x^{2} + 5 x + 14$$$.

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Your Input

Solve $$$x^{4} - 4 x^{3} + 9 x^{2} + 5 x + 14 = 0$$$.

Answer

Root: $$$1 + \frac{\sqrt{-4 - 2 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}} + \frac{30}{\sqrt{-2 + \frac{103}{6 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}} + 2 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}}} - \frac{103}{6 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}}}}{2} - \frac{\sqrt{-2 + \frac{103}{6 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}} + 2 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}}}{2}\approx -0.438532621304825 - 0.981097879600447 i$$$A, multiplicity: $$$1$$$A.

Root: $$$1 - \frac{\sqrt{-2 + \frac{103}{6 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}} + 2 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}}}{2} - \frac{\sqrt{-4 - 2 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}} + \frac{30}{\sqrt{-2 + \frac{103}{6 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}} + 2 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}}} - \frac{103}{6 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}}}}{2}\approx -0.438532621304825 + 0.981097879600447 i$$$A, multiplicity: $$$1$$$A.

Root: $$$1 + \frac{\sqrt{-4 - 2 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}} - \frac{30}{\sqrt{-2 + \frac{103}{6 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}} + 2 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}}} - \frac{103}{6 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}}}}{2} + \frac{\sqrt{-2 + \frac{103}{6 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}} + 2 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}}}{2}\approx 2.438532621304825 - 2.485195999465589 i$$$A, multiplicity: $$$1$$$A.

Root: $$$1 + \frac{\sqrt{-2 + \frac{103}{6 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}} + 2 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}}}{2} - \frac{\sqrt{-4 - 2 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}} - \frac{30}{\sqrt{-2 + \frac{103}{6 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}} + 2 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}}} - \frac{103}{6 \sqrt[3]{\frac{27}{16} + \frac{5 \sqrt{522147} i}{144}}}}}{2}\approx 2.438532621304825 + 2.485195999465589 i$$$A, multiplicity: $$$1$$$A.