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samalbee
samalbee
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Joined: 2021-10-25
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Cubic equations, graphical solving
An approximate solution of a cubic equation can be obtained by substituting the equation - do your homework - in its reduced form x^3+ p x + q= 0 and broken down into two functions as follows:
y=f1 ( x ) =x^3
y=f2 ( x ) = - p x - q  
The graphs of these functions are drawn, the abscissa of their intersection is an approximation for a real solution of the equation.
With a graphical approximation method , one proceeds as follows: One looks at the functiony= f ( x ) =x^3+ ax^2+ b x + c. Because this function always intersects the x-axis at least once (i.e. has a real zero), it is improved by approximation methods - geometry homework help  (e.g. Regula falsi or interval nesting) until the desired accuracy is achieved and the equation is then divided to a quadratic by polynomial division can be traced back. 
A rough approximate solution of a cubic equation is obtained by looking at the equation after using the substitutionx = z-a/3 in the reduced form z^3+ p z+ q= 0 (respectively. x^3+ p x + q= 0) was broken down into two functions.
the end x^3+ p x + q= 0 follows x^3= - p x - q  , and therefore the following functions are considered:
y=f1 (x) =x^3
y=f2 ( x ) = - p x - q  
The graphs of these functions are entered in a coordinate system - do my calculus homework for me , the abscissa of the interface (the point of intersection of the graphs) is an approximation (with reading errors) for a real solution. If necessary, it can be improved by approximation methods.
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