The values for x when f(x) = 0 are:

Question

x=-2 and x=3

My question is:
The function f(x) can be written in the form of a(x-p)(x-q)(x-r)
Write down one possible set of values for p, q, and r?

Now Ive got the correct answer x = -3, 2 and 2

Could you show me step by step how I got that answer?

Answer 1

The values for x when f(x) = 0 are:
x=-2 and x=3

My question is:
The function f(x) can be written in the form of a(x-p)(x-q)(x-r)
Write down one possible set of values for p, q, and r?

Now Ive got the correct answer x = -3, 2 and 2

Could you show me step-by step how to end up with those values?

Do you substitute p, q and r with 0 .

Answer 2

When f(-2)=0 means that (x+2) is a factor of the polynomial.
Similarly, when f(3)=0 means that (x-3) is a factor of the polynomial.

Let a be a mulplicative constant (undetermined), then f(x) is of the form:
f(x) = a(x+2)(x-3)....
Since the question tells us that the function is a cubic, i.e. has three factors, and there are only two distinct roots, the third root must be identical to one of the other two, i.e. the third factor must be either (x+2) or (x-3).
So the two possible answers are:
f(x) = a(x+2)^2(x-3)
or
....
Can you figure out the other one?

Answer 3

By the way, you can look at this link for a sketch of the functions:
http://img41.imageshack.us/img41/9449/adrianat.png