The quadratic equation x^2+2x−8=0 can be rewritten as (x+4)(x−2)=0.
What is the multiplicity of the root x=−4?
A.The multiplicity of the root is 1.
B.The multiplicity of the root is 3.
C.The multiplicity of the root is 2.
D.The multiplicity of the root is 4.
can someone please help I am stuck on this question....
a quadratic only has two roots
You have two factors, so there are two roots, each of multiplicity 1.
If h is a root of multiplicity n, then (x-h)^n is a factor of the polynomial.
(x+4) = (x+4)^1 so -4 has multiplicity 1.
If you were stuck on this, you really need to study the section on your text, or google the topic for examples.
To determine the multiplicity of a root, you need to examine the factored form of the quadratic equation. In this case, the equation is factored as (x+4)(x-2)=0.
The multiplicity of a root is the number of times the root appears as a factor in the equation. In the factored form, each root is associated with one factor. In other words, the multiplicity of a root tells you how many times that root appears as a factor in the equation.
Looking at the factored form (x+4)(x-2)=0, we can see that x=-4 is a root because it causes the first factor (x+4) to become zero. Similarly, x=2 is a root because it causes the second factor (x-2) to become zero.
However, in this case, we are interested in the multiplicity of the root x=-4.
To determine the multiplicity of x=-4, we need to count how many times this root appears as a factor.
In the factored form (x+4)(x-2)=0, we can see that x=-4 appears once as a factor (x+4).
Therefore, the answer is A. The multiplicity of the root x=-4 is 1.