Question

a 4th degree polynomial has roots at -2, 1, and a double root at 5. Write a possible equation.

Answer 1

If a polynomial p of degree n has roots x1,... xp, then
\[
p(x) = K(x-x1)^{r1} (x-x2)^{r2} \cdots (x-xp)^{rp}
\]
Where K is a constant and r1, r2, ... rp are the multiplicity of the corresponding roots.

Answer 2

Can you use the above to solve your problem?

Answer 3

no i don't think so, how do i go from there to an equation?

Answer 4

\[
17 (x-5)^2 (x-1) (x+2) \\
-35 (x-5)^2 (x-1) (x+2)\\
1020 (x-5)^2 (x-1) (x+2)\\
(x-5)^2 (x-1) (x+2)
\]
Any one of the above will do