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  3. Laskurit: Algebra II
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Polynomin $$$f{\left(x \right)} = x^{4} + 6 x^{3} - 3 x^{2} + 17 x - 15$$$ juuret

Laskin yrittää löytää kaikki polynomin $$$f{\left(x \right)} = x^{4} + 6 x^{3} - 3 x^{2} + 17 x - 15$$$ juuret.

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

Syötteesi

Ratkaise $$$x^{4} + 6 x^{3} - 3 x^{2} + 17 x - 15 = 0$$$.

Vastaus

Juuri: $$$- \frac{\sqrt{- \frac{53}{2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}}} + 2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}} + 11}}{2} - \frac{3}{2} + \frac{\sqrt{- 2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}} + \frac{53}{2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}}} + 22 + \frac{106}{\sqrt{- \frac{53}{2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}}} + 2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}} + 11}}}}{2}\approx 0.793705310335777$$$A, kertaluku: $$$1$$$A.

Juuri: $$$- \frac{\sqrt{- 2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}} + \frac{53}{2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}}} + 22 + \frac{106}{\sqrt{- \frac{53}{2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}}} + 2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}} + 11}}}}{2} - \frac{\sqrt{- \frac{53}{2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}}} + 2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}} + 11}}{2} - \frac{3}{2}\approx -6.847415492273561$$$A, kertaluku: $$$1$$$A.

Juuri: $$$- \frac{3}{2} + \frac{\sqrt{- \frac{53}{2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}}} + 2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}} + 11}}{2} + \frac{\sqrt{- \frac{106}{\sqrt{- \frac{53}{2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}}} + 2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}} + 11}} - 2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}} + \frac{53}{2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}}} + 22}}{2}\approx 0.026855090968892 + 1.661100453811431 i$$$A, kertaluku: $$$1$$$A.

Juuri: $$$- \frac{3}{2} + \frac{\sqrt{- \frac{53}{2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}}} + 2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}} + 11}}{2} - \frac{\sqrt{- \frac{106}{\sqrt{- \frac{53}{2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}}} + 2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}} + 11}} - 2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}} + \frac{53}{2 \sqrt[3]{- \frac{271}{16} + \frac{\sqrt{668949}}{16}}} + 22}}{2}\approx 0.026855090968892 - 1.661100453811431 i$$$A, kertaluku: $$$1$$$A.


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