so I am a student of Maths and Physics Track in my school
And in todays class in Maths, the teacher gave us a question. And when no one could solve it, he said that there is going to be a quiz in it tomorrow
I tried to solve it several times but I couldn't solve it
anyways,, the question is
if :: x^3 + ax^2 + bx + c
the rest of dividing it on (x-1) is :: 4
the rest of dividing it on (x+1) is :: -1
find :: a , b , c
The remainder when polynomial f(x) is divided by x-a is f(a). Considering this you get a+b+c = 3 abd a-b+c = 0. So b = 3/2 and a+c = 3/2. You can only have the solution in that form unless you have more information about the concerned polynomial.
The remark of the remainder of f(x) being f(a) when divided by x-a is the statement of the remainder theorem, and the letter a is not the coefficient a of your problem here. The 3 appeared because f(1) = 4 implies 1+a+b+c = 4 which implies a+b+c = 3.
I'm glad I was of help.
a+b+c = 3
a-b+c = 0
2b = 3
=> b = 3/2.
Yes, that works, but so does (a, b, c) = (1, 3/2, 1/2) and many/infinite others. In fact, any a, c ∈ ℝ such that a+c = 3/2 works.a = -2.5
b = 1.5
c = 4
I would leave it in the general form unless the teacher asked only for a pair or you have more restrictions on the given polynomial.