<s>[INST] Need help solving $x^4-3x^3-11x^2+3x+10=0$ Solve $x^4-3x^3-11x^2+3x+10=0$
I have tried to solve this equation using 'general formula from roots' from https://en.wikipedia.org/wiki/Quartic_function.
$$ax^4+bx^3+cx^2+dx+e=0$$
$$x_{1,2}=-\frac b{4a}-S \pm 0.5\sqrt{-4S^2-2P+ \frac q S}$$
$$x_{3,4}=-\frac b{4a} + S \pm 0.5\sqrt{-4S^2-2P-\frac q S}$$
$$p=\frac{8ac-3b^2}{8a^2}$$
$$q= \frac{b^3-4abc+8a^2d}{8a^3}$$
$$S=0.5\sqrt{-\frac{2p} 3 + \frac{Q+\Delta_0} Q}{3a}$$
$$Q=\left(\Delta_1+\sqrt{\Delta_1^2-4\Delta_0^3} \cdot 0.5\right)^{1/3}$$
$$\Delta_0=c^2-3bd+12ae$$
$$\Delta_1=2c^3-9bcd+27eb^2+27ad^2-72ace$$
Those formula does not work. I ended up with complex roots.
Please help me to use those formulas to solve quartic equation. Any help will be very much appreciated.
 [/INST] $$x^4 - 3x^3 - 11x^2 + 3x + 10 = 0$$
$$x^4 - 3x^3 - 10x^2 - x^2 + 3x + 10 = 0$$
$$x^2(x^2 - 3x - 10) - (x^2 - 3x - 10) = 0$$
$$(x^2 - 1)(x^2 - 3x - 10) = 0$$
$$(x - 1)(x + 1)(x - 5)(x + 2) = 0$$
$$x = \{1,-1,5,2\}$$
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