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# Suppose is a polynomial such that , , , and . What is the sum of the coefficients of ?

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Suppose  is a polynomial such that , and . What is the sum of the coefficients of ?

Guest Dec 4, 2014

#1
+92744
+10

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......

CPhill  Dec 4, 2014
#1
+92744
+10

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......

CPhill  Dec 4, 2014
#2
+94110
0

That looks good - I wish I had more time.  I'd love to play with more of these polynomial problems.

There is never enough time when you are having fun

Melody  Dec 4, 2014