Any help with this problem would be appreciated.?

Question

Given the polynomial f(x) = 2x^3 -5x^2 -4x + 3, find all the solutions if the function is completed.


a) f(x) =0

b) f(x+2)=0

d) f(2x) = 0

Answer 1

Let's solve a) first.
We know that for any rational solution a/b
we must have a divides 3 and b divides 2.
Testing values with b = 1, we find that x = -1
is a solution, so x+1 is a factor.
This gives
(x+1)(2x²-7x+3) = 0.
or
(x+1)(2x-1)(x-3) = 0
So the roots of a) are -1, 1/2 and 3.

b) This is the graph of a) shifted left 2 units,
so the roots of b) are -3, -3/2 and 1.

c). The roots of c must be half the roots of a) to
keep the zeros of f the same.
So the roots of c) are -1/2, 1/4 and 3/2.

Answer 2

it is NOT possible. how can many diffrent equations equal to one answer?