+0

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

0
270
2

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

Guest Dec 4, 2014

#1
+81004
+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
Sort:

#1
+81004
+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
+91451
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

### 19 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details