Question

In a equation, how i get to know which root is repeated and the times it repeats, because is tricky when i introduce a 3rd or 4thgrade equation in my calculator and i only get 2 roots

Answer 1

Nice grammar

Answer 2

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Answer 3

do you have a specific example?

Answer 4

@nvafer Graph y = (x -2)² on your calculator and tell us about the roots.

Answer 5

Only way to tell for sure how many times it repeats is by doing synthetic division with the root.

From the graph - you can only tell if it's an even or odd number of repeats.

Answer 6

what i the question

Answer 7

is the question

Answer 8

(m^4)-(7m^3)+(18m^2)-20m+8=0 it has 2 roots my question is the times each of them repeats

Answer 9

\[(m^4)-(7m^3)+(18m^2)-20m+8=0\] there it is folks

Answer 10

@triciaal

Answer 11

@nvafer there are 2 other people here

Answer 12

"Folks"

Answer 13

Look at a graph and you can tell x=1 does not repeat (since it passes straight through), but x=2 does.

Do synthetic division with 2, and repeat the synthetic division until you no longer get a remainder of zero.

Answer 14

Thanks ill try with that

Answer 15

I could not attach graph shows zeros at (1,0) and (2,0)

Answer 16

https://www.desmos.com/calculator

Answer 17

@steve816 I'm a spanish native speaker and I'm not sure if the grammar in the post is correct, so if it's not sarcasm. Thnk you!

Answer 18

@Directrix it has a skngle root: 2

Answer 19

@nvafer

Following @agent0smith 's instructions, can you factor the polynomial?

Answer 20

@Directrix *single root: 2

Answer 21

@Directrix

Answer 22

It could be a single root or a triple root. At m = 2, the graph slices through the x-axis. So, that means it is a root of odd multiplicity. To get to a conclusion, see what the other roots are doing.

By the Fundamental Theorem of Algebra, we have to account for 4 roots of some description.

Answer 23

@nvafer
Look at the graph.

m=1 and m= 2 are roots but of what multiplicity?

We have to account for 4 roots,

For sure, from the graph, these two roots are not of even multiplicity. So, it is not that 1 is a double root and 2 is a double root. That would not be correct.

Answer 24

1 might be a triple root and 2 a single root.

Or,

1 might be a single root and 2 and triple root.

Answer 25

Look at the factorization you posted.

Answer 26

(m - 2)² * (m-1) = 0

That is a key to which root is triple and which is singular. @nvafer

Answer 27

@Directrix single roots always have the characteristic passes-straight-through-the-axis look to them, so you can always eliminate them as repeated roots.

Triple or higher odd numbers have the passing-through-with-a-flat-portion look.

Answer 28

"playing with the results "
m^4 means 4 roots
m-1 is taken and goes through
constant is 8 consider m^3 therefore 2 is the triple root

Answer 29

Thanks. @agent0smith

@nvafer

Even multiplicity roots look like this on a graph.

They are located at points of tangency of the graph to the x-axis

Bounce points, I call them.