Question

The quadratic equation x2 + 2x -- 8 = 0 can be rewritten as (x + 4)(x - 2) = 0.

What is the multiplicity of the root x = --4?

Answer 1

multiplicity of 1

Explanation:

Given the roots of an equation are

x = - 4 ← multiplicity 1

(x + 4)² = 0

x + 4 = 0 or x + 4 = 0 , hence

x = - 4 or x = - 4 , that is

x = - 4 ← with multiplicity 2

(x + 4)³ = 0

has roots x = - 4 with multiplicity 3

The multiplicity is determined by the exponent the factor is raised to