Question

Find the polynomial f(x) that has the roots of -2, 5 of multiplicity 2. Explain how you would verify the zeros of f(x).

Answer 1

A root or zero is given by: \[x=a \\ x-a=0\]
so \[x=-2\hspace{0.5cm}\Rightarrow \;x+2=0 \\ x=5\hspace{0.5cm}\Rightarrow \;x-5=0\]
so these are the two factors of the polynomial.
Now multipilcity gives you the exponent of them:
\[p(x)=(x+2)^2(x-5)^2\]