Question

5. Find the polynomial function with roots 1, 7, and -3 of multiplicity 2.

Answer 1

given a set of roots: \(r_1,r_2,r_3,r_4,...,r_n\)

a poly can be created by simply subtracting x from each root and multiplying the whole thing together

Answer 2

\[P_n(x)=(r_1-x)(r_2-x)(r_3-x)(r_4-x)...(r_n-x)\]

Answer 3

f(x) = y = (x - 1)^2 times (x - 7)^2 times ( x + 3)^2

Now, you expand the right side if you are required. This equation gives a multiplicity of 2 for each of the 3 factors.