Question

find polynomial f x of degree 3 that has the roots of -3,5 of multiplicity 2. Explain how you would verify the zero of f(x).

Answer 1

f(x)

Answer 2

roots of -3, 5 and 5 mean that f(x) has the following factors:
(x+3),(x-5),(x-5)
so the polynomial expression that fits this criteria is:
\[f(x)=a(x+3)(x-5)^2\]where a=any non-zero constant. Choose a=1 for simplest case.