+1756 Let f be a cubic polynomial such that f(0) = 5, f(2) = 8, f(3)=13, and f(7) = -5. What is the sum of the coefficients of f?
+129830 f(0) = 5, f(2) = 8, f(3)=13, and f(7) = -5
We have the form
ax^3 + bx^2 + cx + d
Since f(0) = 5 then d = 5
We have this system
a(2)^3 + b(2)^2 + c(2) + 5 = 8
a(3)^3 + b(3)^2 + c(3) + 5 = 13
a(7)^3 + b(7)^2 + c(7) + 5 = -5 simplify
8a + 4b + 2c = 3
27a + 9b + 3c = 8
343a +49b + 7c = -10
I'm assuming that you know how to solve such a system
a = -46/105 = -92/210
b = 47/14 = 705/210
c = -727/210
Sum of coefficients = [-92 + 705 - 727 ] / 210 = -114 / 210 = -57 / 105
