#help

88 messages · Page 1 of 1 (latest)

empty orioleBOT
grave pelican
#

find where the zeroes are

sullen coyote
#

ye its 3 and -1

grave pelican
#

like 4 of them have the same zeroes

rose ermine
#

yuh

grave pelican
#

the next step is to see the multiplicty of the zeroes

sullen coyote
#

english

grave pelican
#

actually, you should look at the leading coefficient first and degree

#

what is the degree and sign of the leading coefficient?

sullen coyote
#

like -2^3

rose ermine
grave pelican
#

-2^3 is -8

uncut obsidian
grave pelican
#

-2 is the leading coefficient

sullen coyote
#

degree is odd sign negative

grave pelican
#

but why is -2 being cubed

#

degree is not odd

#

look at all the exponents of the factors and add them up

sullen coyote
#

ye its 3

grave pelican
#

actually, you don't even need to worry about multiplicity of roots

grave pelican
#

(x-3)^3 and (x+1)^1

rose ermine
#

implied ^1 btw

grave pelican
#

maybe you thought no exponent meant 0?

#

but it means it is raised to the first power

sullen coyote
#

yea

grave pelican
#

so even degree, negative leading coefficient, with zeroes at x=3 and -1

sullen coyote
#

ok so its -2^4?

grave pelican
sullen coyote
#

its B or C

grave pelican
#

does C look like it has x=3 as a zero?

sullen coyote
#

i guess not

grave pelican
#

both the zeroes are negative for C right?

sullen coyote
#

yea

uncut obsidian
# sullen coyote ok so its -2^4?

(dont consider the leading coefficient to be raised to the power of [degree], since technically they are both their own things that control their own stuff)

grave pelican
#

the leading coeffieicient is not being raised to the degree of the polynomial

#

if the -2 was inside the parathesis in like (-2x+4)^4

#

then the leading coefficient would be (-2)^4

#

but that's not the case here

sullen coyote
#

so its B

grave pelican
#

so how many of that factor can you divide out while still having a polynomial

grave pelican
sullen coyote
#

thank you daddy

#

i understand now

grave pelican
uncut obsidian
sullen coyote
uncut obsidian
#

not for this specific problem

grave pelican
#

in this example, you didn't have to worry about multiplicity bc there the leading coeff, degree and zeroes were enough

uncut obsidian
#

but based on the format im guessing its a necessary skill for you

sullen coyote
#

alr

#

thanks gentlemen

#

oh shit the post didnt delete

grave pelican
sullen coyote
#

i just lost aura

grave pelican
#

here is an example of where you would need to use multiplicity

#

the first equation with -2(x-3)^3(x+1), which was in the original example, can you tell if that is the blue or red graph?

sullen coyote
#

prolly red

grave pelican
#

no

sullen coyote
#

i guessed

grave pelican
#

(x-3) is cubed, so at x=3 the multiplicty should be 3

#

which means if you zoom in at x=3, it'll look like a cubic

sullen coyote
#

fuck is a cubic

grave pelican
#

it flattens out before continuing the current direction

#

by direction, i mean increasing or decreasing

#

technically, it's the sign of the slope

#

the red one, when it passes x=3, you see how it looks like a straight line?

sullen coyote
#

yea

grave pelican
#

that means the multiplicyt is just 1, since lines have a degree of 1

#

so you'd expect (x-3) to be raised to power of 1

#

for the red graph

#

if at x=a, the graph passes through it like a line, the multiplicity is 1, so it's just (x-a)

#

if it passes like a parabola, then multiplicity is 2, so it'd be (x-a)^2

#

if it passes like a cubic, it'd have multiplicity 3, so it'd be (x-a)^3

#

usually, multiplicites will only be 1, 2, or 3. They won't give you a mult. of 4, because it''s very hard to tell the difference between a multiplicity of 4 vs a mult of 2

#

since both will appear to "bounce" off the x-axis

sullen coyote
#

yo ur smart

grave pelican
#

well, i am in 12th grade

#

but math is my best subject

#

algebra and calculus

sullen coyote
#

thank you uncle

#

i will be closing this now

grave pelican
#

alright, good night

#

well it's night for me

sullen coyote
uncut obsidian