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Let $f$ be a cubic polynomial such that $f(0) = 5$, $f(1) = -5$, $f(2) = 8$, and $f(3)=13$. What is the sum of the coefficients of $f$?

frozensssss Dec 6, 2024

eramsby1O1O · Answer 1 · 2024-12-07T12:07:47

Using polynomial interpolation, we can find that f(x) = -17/3*x^3 + 59/2*x^2 - 209/6*x + 5.

Therefore, the sum of the coefficients is -17/3 + 59/2 - 209/6 = -11.

Hope this helps!