Suppose is a polynomial such that , , , and . What is the sum of the coefficients of ?
This polynomial has - at least - two real zeroes.....(there may be more).....let's suppose that it's a cubic
So we have
f(x) = ax^3 + bx^2 + cx + d ....Note, "d" has to be equal to 47
So we have this system
a(1)^3 +b(1)^2 + c(1) + 47 = 32
a(2)^3 +b(2)^2 + c(2) + 47 = -13
a(3)^3 +b(3)^2 + c(2) + 47 = 16
We can simplify these to:
a + b + c = -15
8a + 4b + 2c = -60
27a + 9b + 3c = -31
I used WolframAlpha solve this one .... (I'm lazy.....)
a = 52/3 b = -67 c = 104/3 d = 47..... I'll let you sum these.......!!!!
Here's the graph.........https://www.desmos.com/calculator/gnbrhqhxdr
(Yep...that works !!!!)
Note that - if this is a cubic - there had to be another real zero...also, this solution may not be unique....other functions might be possible......
Suppose is a polynomial such that , , , and . What is the sum of the coefficients of ?
This polynomial has - at least - two real zeroes.....(there may be more).....let's suppose that it's a cubic
So we have
f(x) = ax^3 + bx^2 + cx + d ....Note, "d" has to be equal to 47
So we have this system
a(1)^3 +b(1)^2 + c(1) + 47 = 32
a(2)^3 +b(2)^2 + c(2) + 47 = -13
a(3)^3 +b(3)^2 + c(2) + 47 = 16
We can simplify these to:
a + b + c = -15
8a + 4b + 2c = -60
27a + 9b + 3c = -31
I used WolframAlpha solve this one .... (I'm lazy.....)
a = 52/3 b = -67 c = 104/3 d = 47..... I'll let you sum these.......!!!!
Here's the graph.........https://www.desmos.com/calculator/gnbrhqhxdr
(Yep...that works !!!!)
Note that - if this is a cubic - there had to be another real zero...also, this solution may not be unique....other functions might be possible......