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3d.sk Modeling Image References Download
This is a collection of 3D Human and Animal references for 3DS Max, Autodesk Maya and Blender.
A collection of nude, clothed and funny human and animal anatomy model references.Q:
What’s the answer for my solution of $X^{3}-5X-4=0$
$\mathbf{Question:}$ Solve the equation $$X^{3}-5X-4=0$$ using the trinomial theorem.
$\mathbf{My\, solution:}$ I got $X=1, X=\frac{ -1\pm \sqrt{17}}{2}$. To find the sign of the square root, I calculated the discriminant and it gives $-31$
Why do they have different signs?
A:
Note that
$$(X^3 – 5X – 4) = (X-1)(X^2 + 3X + 4)$$
so the roots are the roots of the monic polynomial $(X-1)(X^2 + 3X + 4)$.
The first factor is $$X-1=(-1)(-1+\sqrt{17})=-\sqrt{17}+1$$
so the first root is $-1-\sqrt{17}$.
The second factor is
$$X^2 + 3X + 4 = (X+1)^2 -2 = X^2 – 3X – 2$$
so the second root is
$$X+1 = \sqrt{3}\cdot\sqrt{X^2 – 3X – 2}.$$
So the second root is
$$-1 + \sqrt{17} = \sqrt{3}\cdot\sqrt{\sqrt{17}-2}.$$
Note that this is one of the roots of $x^2 – 3x – 2$, so the correct sign is given by its discriminant.
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