Question

Find the polynomial f(x) that has the roots of -2, 3 of multiplicity 2. Explain how you would verify the zeros of f(x).

Answer 1

There are plenty of solutions for this, but the most basic would be
\[f(x)=(x+2)(x-3)^2\]
Roots are zeroes. That means if you plug in -2, you'll get 0:
\[f(-2)=\color{red}{(-2+2)}(-2-3)^2=0\]