Question

Find a polynomial equation that has zeros at x = -2, x = 3 and a double root at x = 5

Answer 1

If x=k is a zero of a polynomial, then (x-k) is a factor in the polynomial.

So with roots at x = -2 , x = 3, and x = 5, you have

(x+2)·(x-3)·(x-5)

Now the "double root" means that you have that factor twice

(x+2)·(x-3)·(x-5)·(x-5)

but we'd normally write that with an exponent:

(x+2)·(x-3)·(x-5)^2

So y = (x+2)·(x-3)·(x-5)^2 is your equation.