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Lagrange's method can be applied directly to the general cubic equation ax 3 + bx 2 + cx + d = 0, but the computation is simpler with the depressed cubic equation, t 3 + pt + q = 0. Lagrange's main idea was to work with the discrete Fourier transform of the roots instead of with the roots themselves.
In mathematics, a cubic plane curve is a plane algebraic curve C defined by a cubic equation F ( x , y , z ) = 0 {\displaystyle F(x,y,z)=0} applied to homogeneous coordinates ( x : y : z ) {\displaystyle (x:y:z)} for the projective plane ; or the inhomogeneous version for the affine space determined by setting z = 1 in such an ...
In mathematics, a cubic surface is a surface in 3-dimensional space defined by one polynomial equation of degree 3. Cubic surfaces are fundamental examples in algebraic geometry . The theory is simplified by working in projective space rather than affine space , and so cubic surfaces are generally considered in projective 3-space P 3 ...
Graph of the polynomial function x 4 + x 3 – x 2 – 7x/4 – 1/2 (in green) together with the graph of its resolvent cubic R 4 (y) (in red). The roots of both polynomials are visible too. In algebra, a resolvent cubic is one of several distinct, although related, cubic polynomials defined from a monic polynomial of degree four:
The roots, stationary points, inflection point and concavity of a cubic polynomial x 3 − 6x 2 + 9x − 4 (solid black curve) and its first (dashed red) and second (dotted orange) derivatives. The critical points of a cubic function are its stationary points , that is the points where the slope of the function is zero. [ 2 ]
Cubic crystal system, a crystal system where the unit cell is in the shape of a cube; Cubic function, a polynomial function of degree three; Cubic equation, a polynomial equation (reducible to ax 3 + bx 2 + cx + d = 0) Cubic form, a homogeneous polynomial of degree 3; Cubic graph (mathematics - graph theory), a graph where all vertices have ...
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