Question 640281
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A cubic polynomial function in standard form is:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ f(x)\ =\ ax^3\ +\ bx^2\ +\ cx\ +\ d]


So if *[tex \LARGE f(2)\ =\ 36], then


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ a(2)^3\ +\ b(2)^2\ +\ c(2)\ +\ d\ =\ 36]


which is to say:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 8a\ +\ 4b\ +\ 2c\ +\ d\ =\ 36]


Likewise, from the other function values given:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -64a\ +\ 16b\ -\ 4c\ +\ d\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 0a\ +\ 0b\ +\ 0c\ +\ d\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 27a\ +\ 9b\ +\ 3c\ +\ d\ =\ 0]


But from the third equation, this reduces to the 3X3 system:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 8a\ +\ 4b\ +\ 2c\ =\ 36]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ -64a\ +\ 16b\ -\ 4c\ =\ 0]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 27a\ +\ 9b\ +\ 3c\ =\ 0]


Just solve the 3X3 by any convenient means to find the coefficients of your cubic function.


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
My calculator said it, I believe it, that settles it
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