Question

Find the root(s) of f (x) = (x + 5)3(x - 9)2(x + 1).

Answer 1

answer:

a. -5 with multiplicity 3  

d. 9 with multiplicity 2

f. -1 with multiplicity 1

hope this helps! :o)

Answer 2

The roots of a polynomial written in the form

$(x-x_1)(x-x_2)(x-x_3)\ldots(x-x_n)$

Are exactly

$x_1,\ x_2,\ x_3,\ldots x_n$

The multiplicity of a solution $x_i$ is how many times the parenthesis $(x-x_i)$ appears in the factorization of the polynomial.

So, if we write the powers explicitly, your polynomial is written as

$(x + 5)^3(x - 9)^2(x + 1) = (x + 5)(x + 5)(x + 5)(x - 9)(x - 9)(x + 1)$

Which means that the solutions are:

• -5, with multiplicity 3
• 9, with multiplicity 2
• -1, with multiplicity 1