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["#exemples pour le calcul des coefficients d'un polynôme à travers des points"]
["(voir pour calcul avec R: exemples_polynome_travers_points.r)"]
["#deux points déterminent une droite "]
["#(2,3), (4,7)"]
["x^0","x^1",null,"f(x)"]
[1,2,null,3]
[1,4,null,7]
[]
["matrice inverse",null,null,"solution du système d'équations:"]
[2,-1,null,-1,"a0"]
[-0.5,0.5,null,2,"a1"]
["# polynôme: f(x)=2x-1"]
[]
[]
["#trois points déterminent un polynôme du deuxième degré (sous conditions ...)"]
["#(3,3), (4,7), (5,9)"]
["x^0","x^1","x^2",null,"f(x)"]
[1,3,9,null,3]
[1,4,16,null,7]
[1,5,25,null,9]
[]
["matrice inverse",{"$nulls":3},"solution du système d'équations:"]
[10,-15,6,null,-21,"a0"]
[-4.5,8,-3.5,null,11,"a1"]
[0.5,-1,0.5,null,-1,"a2"]
["#polynôme: f(x)= -x^2+11x-21"]
[]
[]
["#quatre points déterminent un polynôme du troisième degré (sous conditions ...)"]
[]
["#(3,3),(4,7), (5,9), (10,1)"]
["x^0","x^1","x^2","x^3 ",null,"f(x)"]
[1,3,9,27,null,3]
[1,4,16,64,null,7]
[1,5,25,125,null,9]
[1,10,100,1000,null,1]
[]
["matrice inverse",{"$nulls":4},"solution du système d'équations:"]
[14.28571428571428,-25,11.999999999999998,-0.2857142857142853,null,-24.428571428571466,"a0"]
[-7.857142857142855,15.833333333333334,-8.2,0.22380952380952351,null,13.6857142857143,"a1"]
[1.3571428571428572,-3,1.7,-0.057142857142857086,null,-1.6857142857142888,"a2"]
[-0.07142857142857144,0.16666666666666666,-0.09999999999999999,0.004761904761904759,null,0.057142857142857065,"a3"]
[]
["#polynôme: f(x)=0.05714286x^3-1.68571429x^2+13.68571429x-24.42857143"]
[]
[]
["#cinq points déterminent un polynôme du quatrième degré (sous conditions ...)"]
["#(3,3),(4,7), (5,9), (10,1), (12,50)"]
["x^0","x^1","x^2","x^3 ","x^4",null,"f(x)"]
[1,3,9,27,81,null,3]
[1,4,16,64,256,null,7]
[1,5,25,125,625,null,9]
[1,10,100,1000,10000,null,1]
[1,12,144,1728,20736,null,50]
["matrice inverse",{"$nulls":5},"solution du système d'équations:"]
[19.047619047619033,-37.5,20.57142857142861,-1.7142857142857126,0.5952380952380949,null,7.8333333333336235,"a0"]
[-12.063492063492058,26.875,-15.771428571428588,1.4857142857142844,-0.5257936507936505,null,-14.812301587301707,"a1"]
[2.6825396825396823,-6.479166666666667,4.085714285714287,-0.45476190476190453,0.1656746031746031,null,7.293849206349218,"a2"]
[-0.24603174603174602,0.625,-0.4142857142857143,0.05714285714285713,-0.02182539682539682,null,-1.1257936507936506,"a3"]
[0.007936507936507936,-0.020833333333333332,0.014285714285714285,-0.0023809523809523807,0.000992063492063492,null,0.05376984126984127,"a4"]
[]
[]
[]
["#polynôme: f(x)=   0.05376984x^4-1.12579365x^3+7.29384921x^2-14.81230159x+7.83333333"]

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