Construct a polynomial function of least degree possible using the given information. Real roots: −1 (with multiplicity 2), 1 and (2, f(2)) = (2, 4)

Question

Construct a polynomial function of least degree possible using the given information.

Real roots: −1 (with multiplicity 2), 1 and (2, f(2)) = (2, 4)

Answer 1

Okay, first I think that there is a small parallelism error in the stating of the problem. My instincts say that I need to make it clear that the real roots are -1, -1, 1 with f(2)=4. There are two -1's because of the multiplicity.

Every root is a root that has a factor of (x - root) So the polynomial should look like this:

f(x)= a(x+1)(x+1)(x-1) From this I would find the a value by plugging in 2 and 4

4 = a(2+1)²(2-1)

4 = 9a Thus a = 4/9

Depending upon the teacher f(x) = (4/9)(x+1)²(x-1) could be enough of an answer. However some might want you to foil it out.

f(x) = (4/9)x³ - (4/3)x² + (8/9)x - (4/9)

Hope this helps.