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  3. Laskurit: Algebra II
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Polynomin $$$f{\left(x \right)} = x^{4} - 4 x^{3} + 9 x^{2} + 5 x + 14$$$ juuret

Laskin yrittää löytää kaikki polynomin $$$f{\left(x \right)} = x^{4} - 4 x^{3} + 9 x^{2} + 5 x + 14$$$ juuret.

Jos laskin ei laskenut jotakin tai olet havainnut virheen tai sinulla on ehdotus tai palaute, ole hyvä ja ota meihin yhteyttä.

Syötteesi

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

Vastaus

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

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

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

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


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