SOLUTION: Find a polynomial of the form f(x)=ax3+bx2+cx+d such that f(0)=2, f(2)=−2, f(−3)=−2, and f(−5)=7. Answer: f(x)=

Question 1176848: Find a polynomial of the form f(x)=ax3+bx2+cx+d such that f(0)=2, f(2)=−2, f(−3)=−2, and f(−5)=7.
Answer: f(x)=
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
f(x)=ax^3+bx^2+cx+d, and d=2, when x=0
f(2)=8a+4b+2c+2=-2 or 8a+4b+2c+4=0 or 4a+2b+c+2=0
f(-3)=-27a+9b-3c+2=-2 or -27a+9b-3c+4=0
f(-5)=-125a+25b-5x+2=7 or -25a+5b-c-1=0, collecting terms and dividing by 5
from the first and last
4a+2b+c=-2
-25a_5b-c=1
-21a+7b=-1
from the second and last
-27a+9b-3c=-4
75a-15b+3c=-3
48a-6b=-7
There are now two equations in 2 unknowns.
You will obtain a=-11/42 (keep it in fractional form)
b=-13/14
and c=19/21
and this is one form of the desired polynomial.

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