數值分析問題(求次数小于等于3的多项式)

Let P(x)=a*x^3+b*x^2+c*x+d
Then
P’(x)=3a*x^2+2b*x+c
P’’(x)=6a*x+2b

From the given four conditions, we can obtain:
P(x0)=a*(x0)^3+b*(x0)^2+c*(x0)+d …..(1)
P(x1)=a*(x1)^3+b*(x1)^2+c*(x1)+d ……(2)
P’(x0)=3a*(x0)^2+2b*(x0)+c ……(3)
P’’(x0)=6a*(x0)+2b ……(4)

By solving the four simultaneous equations, the unknown coefficients a, b, c, d can be found provided a solution does exist.

Let p(x) to be a generic cubic polynomial.
Substitute the values in
Solve the 4 linear equations with 4 unknown
Done.