Question

HELP NEE

Answer 1

do you want the graph

Answer 2

no i just need to know how to solve this one i have desmos if i want to graph but i need to know how

Answer 3

A zero is someplace the graph wold cross the x-axis (in other words, where y is zero). Multiplicity says how many times that solution appears in the eequation.

Answer 4

one post of how to do it would be great, because this is how I learn these are my examples so if you could tell me the steps that would be awesome

Answer 5

what could I do with that next ??

Answer 6

Suppose you had y = (x - 3)^3(x - 1)^2(x+1)

Answer 7

so I would make them into 0's or equaling 0's right

Answer 8

Do you agree that for y to be 0, that either y = (x - 3)^3 =
or (x - 1)^2 = 0
or (x+1) = 0
right?

the only way for 2*x = 0 to be true is if x = 0.
And the only way fro x*y = 0 is for x=0 or y=0.

Answer 9

So if you mean "set each term in parentheses equal to zero", yes, that is right.

Answer 10

So don't worry about multiplicity for a moment, just tell me what the zeros are for your equation.

Answer 11

how to i find the zeros... sorry!

Answer 12

The zeros for my equation, y = (x - 3)^3(x - 1)^2(x+1)
are 3, 1, and -1

because 3-3 is zero, so when x=3, the equation becomes 0*12*4, which is zero.

Answer 13

oh ok so mine would be -5,-64, and 512?

Answer 14

Take a term, set it to zero, find x:

Your first term is (x + 8)^2
Set it to zero
(x + 8)^2 = 0
x+8 = 0
x+8 -8 = 0-8
x=-8

Got it?

Answer 15

yes i got that

Answer 16

what next? @mjdennis

Answer 17

There is another zero. What is that value?

Answer 18

I'll go back to my example to explain multiplicity.

y = (x - 3)^3(x - 1)^2(x+1)

The three zeros are 3, 1, -1

But because we have (x-3)^3 , which is (x-3)(x-3)(x-3), and (x-1)^2, my problem really has six answers
3,3,3,1,1,-1
even though some are duplicates of each other, there are soem parts of math where you will need to know how many times a dupe answer appears.

so the example has zeros (3 multiplicity 3), (1multiplicity 2), and (1 multiplicity 1). That last one we can just shorten to "1"

Answer 19

x=3

Answer 20

my other "0"