SOLUTION: If F(x) = ax^2+bx+c, and F(x+5) = x^2+9x-7, find the sum of a+b+c. a) -27 b) 0 c) 21 d) -21 e) 27

Algebra ->  Rational-functions -> SOLUTION: If F(x) = ax^2+bx+c, and F(x+5) = x^2+9x-7, find the sum of a+b+c. a) -27 b) 0 c) 21 d) -21 e) 27      Log On


   

Question 1170374: If F(x) = ax^2+bx+c, and F(x+5) = x^2+9x-7, find the sum of a+b+c.
a) -27
b) 0
c) 21
d) -21
e) 27
Answer by ikleyn(52906) About Me  (Show Source):
You can put this solution on YOUR website!
.

The sum   a + b + c  is the value F(1)  of the polynomial  F(x), when the argument is equal to 1.


In order for the argument would be 1 in F(x+5), we should take x= -4.


THEREFORE,  a + b + c = F(1) = F(-4 +5) = %28-4%29%5E2+%2B+9%2A%28-4%29+-+7 = -27.    ANSWER

Solved.