Question

What is a double root and a triple root? I am graphing ana dI am suppose to have at least 5 touches to the x-axis with multiplicity of at least one double root and one triple root

Answer 1

Multiplicity is the number of times the same root appears.

Here is an example.
Let's say you have equation

\(x^2 + 3x + 2 = 0\)

You factor it into

\((x + 2)(x + 1) = 0\)

and you get roots

\(y = -2\) or \(x = -1\)

Ok so far?

Answer 2

Each of the above roots only appears once, so the multiplicity of each root is 1.

Now let's say you have a 3rd-degree polynomial that factors into

\((x + 2)(x + 2)(x + 1) = 0\)

By applying the zero-product rule, you continue to solve it like this:

x + 2 = 0 or x + 2 = 0 or x + 1 = 0

x = -2 or x = -2 or x = -1

Notice that the root x = -2 appears twice, so you can say the solutions are

x = -2 with multiplicity 2 or x = -1

Answer 3

A polynomial equation has as many solutions as the degree of the polynomial.
For example, a 5th degree polynomial has 5 solutions.
If the polynomial equation is

\((x - 10)^5 = 0\)

Then the solution is

x = 10 with multiplicity 5,

meaning there are 5 solutions, but they're all the same, x = 10.

Answer 4

A double root is a root with multiplicity 2, and a triple root is a root with multiplicity 3.

Answer 5

okay thank you! When graphing how does that apply? because it can only hit, let's say -2, once.

Answer 6

what does a 5th degree poly look like when graphed?

Answer 7

at least 5 touches .... so it can be greater than degree 5

Answer 8

pick 2 values to be the triple and double roots, then pick 3 more values to hit the x axis whereever you please

Answer 9

y=(x-a)^3 (x-b)^2 (x-c) (x-d) (x-e)

it has 5 places it touches the x axis, and has multiplicity of roots required