Mimi_x3
Can you please help me with this maths question
1. The cubic polynomial P(x)= x^3 +rs^2 +sx+t , where r,s and t are real numbers has three real zeroes,1,a, and -a
(a) find the value of s + t
Delete
Share
This Question is Closed
myininaya
Best Response
You've already chosen the best response.
1
is the polynomial written correctly?
Mimi_x3
Best Response
You've already chosen the best response.
4
woops my bad sorry
P(x) = x^3 +rx^2 +sx +t
helpme1234
Best Response
You've already chosen the best response.
0
Colorful pi can you help me?
myininaya
Best Response
You've already chosen the best response.
1
let me try to help him and then i will look at your question
Mimi_x3
Best Response
You've already chosen the best response.
4
him ? are yu referring to me ?
myininaya
Best Response
You've already chosen the best response.
1
is this algebra?
Mimi_x3
Best Response
You've already chosen the best response.
4
noo , its a polynomial question
myininaya
Best Response
You've already chosen the best response.
1
so what class is it then?
Mimi_x3
Best Response
You've already chosen the best response.
4
class ? what do yu mean ? Its from the topic polynomials
myininaya
Best Response
You've already chosen the best response.
1
\[P(x)=(x-1)(x-a)(x+a)=x^3+rs^2+sx+t\]
Mimi_x3
Best Response
You've already chosen the best response.
4
is that the answer ?
myininaya
Best Response
You've already chosen the best response.
1
so I guess you are doing it for fun?
\[P(x)=(x-1)(x^2-a^2)=x^3+rs^2+sx+t\]
no i just thought u would like to see the steps
Mimi_x3
Best Response
You've already chosen the best response.
4
no , im not doing it for fun , its my maths assignment LOL
myininaya
Best Response
You've already chosen the best response.
1
\[P(x)=x(x^2-a^2)-1(x^2-a^2)=x^3+rsx^2+sx+t\]
myininaya
Best Response
You've already chosen the best response.
1
so the class is called polynomials lol?
Mimi_x3
Best Response
You've already chosen the best response.
4
what does yu mean by class ?
myininaya
Best Response
You've already chosen the best response.
1
\[P(x)=x^3-a^2x-x^2+a^2=x^3+rsx^2+sx+t\]
people go to class to learn and get assignments lol
Mimi_x3
Best Response
You've already chosen the best response.
4
no the class is called maths LOL
myininaya
Best Response
You've already chosen the best response.
1
\[P(x)=x^3-x^2-a^2x+a^2=x^3+rsx^2+sx+t\]
Mimi_x3
Best Response
You've already chosen the best response.
4
2 unit maths to be specific
myininaya
Best Response
You've already chosen the best response.
1
ok we are almost done with this problem
can you guess what to do next?
myininaya
Best Response
You've already chosen the best response.
1
we want both sides to be the same
Mimi_x3
Best Response
You've already chosen the best response.
4
collecting like terms ?
myininaya
Best Response
You've already chosen the best response.
1
ok the the coefficient of x^2 on left hand side is -1
the coefficient of x^2 on the other sides is rs
so what can you say about rs and -1?
myininaya
Best Response
You've already chosen the best response.
1
they must be equal
myininaya
Best Response
You've already chosen the best response.
1
so we need that for the other terms as well
myininaya
Best Response
You've already chosen the best response.
1
we have
-1=rs
-a^2=s
a^2=t
polpak
Best Response
You've already chosen the best response.
0
I seriously think I'm being trolled here.. but just to ease my tired brain..
\[\sqrt{25} \ne -5\]
myininaya
Best Response
You've already chosen the best response.
1
you are right polpak
Mimi_x3
Best Response
You've already chosen the best response.
4
wait , dnt yu factorise it further to (x^2-a^2)(x-1)
myininaya
Best Response
You've already chosen the best response.
1
that =5
myininaya
Best Response
You've already chosen the best response.
1
factor?
polpak
Best Response
You've already chosen the best response.
0
Someone was trying to tell me that it equals both 5 and -5
myininaya
Best Response
You've already chosen the best response.
1
ok the objective is to find s+t
polpak
Best Response
You've already chosen the best response.
0
But I can only really prove it by going to the definition. Which they don't accept.
Mimi_x3
Best Response
You've already chosen the best response.
4
ohh yeah , my bad
polpak
Best Response
You've already chosen the best response.
0
Sorry for bothering you mimi, but myin rarely watches group chat (with good reason)
myininaya
Best Response
You've already chosen the best response.
1
what do you think s+t is based on what i gave you above?
hint we don't need that first equation rs=-1
Mimi_x3
Best Response
You've already chosen the best response.
4
yu talking to me or polpak ? LOL
myininaya
Best Response
You've already chosen the best response.
1
you
Mimi_x3
Best Response
You've already chosen the best response.
4
lols , tbh im lost , i dont get it xDD
myininaya
Best Response
You've already chosen the best response.
1
do you understand when I wrote P
as P(x)=(x-1)(x-a)(x+a)?
Mimi_x3
Best Response
You've already chosen the best response.
4
yeah , i dont understand the part
-1 = rs
-a^2 = s
a^2 = t
where did yu get it from ?
myininaya
Best Response
You've already chosen the best response.
1
both sides had to be equal we were looking at
\[P(x)=x^3-a^2x-x^2+a^2=x^3+rsx^2+sx+t \]
myininaya
Best Response
You've already chosen the best response.
1
look at the coefficients of each term on both sides
we want each term to be the same as it is on the other side
myininaya
Best Response
You've already chosen the best response.
1
so if we look at the x^3's they are good
they both have coefficient 1
what is the coefficient of x^2 on left hand side ?
what is the coefficient of x^2 on right hand side?
Mimi_x3
Best Response
You've already chosen the best response.
4
ohh i get it
rs = -1
myininaya
Best Response
You've already chosen the best response.
1
yes
now
what is the coefficient of x on the left hand side?
what is the coefficient of x on the right hand side?
Mimi_x3
Best Response
You've already chosen the best response.
4
x on the left hand side: 1 i think
x on the right hand side 1 i think
myininaya
Best Response
You've already chosen the best response.
1
no what is the number in front of x on boths?
myininaya
Best Response
You've already chosen the best response.
1
both sides*
Mimi_x3
Best Response
You've already chosen the best response.
4
there's no other number
myininaya
Best Response
You've already chosen the best response.
1
-a^2?
s?
Mimi_x3
Best Response
You've already chosen the best response.
4
lols , its a letter not a number
myininaya
Best Response
You've already chosen the best response.
1
they are numbers
Mimi_x3
Best Response
You've already chosen the best response.
4
they are ? arent they are called pronumerals ?
Mimi_x3
Best Response
You've already chosen the best response.
4
are they*
myininaya
Best Response
You've already chosen the best response.
1
never heard of this term
Mimi_x3
Best Response
You've already chosen the best response.
4
ohh ok
myininaya
Best Response
You've already chosen the best response.
1
when you are doing math and you don't see a word and you see a letter it usually represents a number unless it is the word a or i
myininaya
Best Response
You've already chosen the best response.
1
becauce a and i can be words
Mimi_x3
Best Response
You've already chosen the best response.
4
ohh ok , i never knew that they are numbers xD
myininaya
Best Response
You've already chosen the best response.
1
but usually the book will make it clear to you what they are
myininaya
Best Response
You've already chosen the best response.
1
yep
Mimi_x3
Best Response
You've already chosen the best response.
4
ok , so x= a^3
myininaya
Best Response
You've already chosen the best response.
1
a^3 is nowhere to be found
we aren;t solving equation for x
Mimi_x3
Best Response
You've already chosen the best response.
4
ok , so x= a^3
Mimi_x3
Best Response
You've already chosen the best response.
4
ohh ok
myininaya
Best Response
You've already chosen the best response.
1
ok so look again at the polynomial
what is the coefficent of x on both sides?
Mimi_x3
Best Response
You've already chosen the best response.
4
ok , so x= a^3
Mimi_x3
Best Response
You've already chosen the best response.
4
ok , so x= a^3
Mimi_x3
Best Response
You've already chosen the best response.
4
x= s
myininaya
Best Response
You've already chosen the best response.
1
ok no
\[P(x)=x^3-a^2x-x^2+a^2=x^3+rsx^2+sx+t \]
^ ^
| |
-a^2 = s
Mimi_x3
Best Response
You've already chosen the best response.
4
ok , so x= a^3
Mimi_x3
Best Response
You've already chosen the best response.
4
ohh lols , sorry im so slow of understanding it
myininaya
Best Response
You've already chosen the best response.
1
ok do you see the terms that don't an x in em?
there terms are called constants and they must be equal of that we have the same polynomial on both sides
myininaya
Best Response
You've already chosen the best response.
1
god my english is getting bad
Mimi_x3
Best Response
You've already chosen the best response.
4
ok , so x= a^3
Mimi_x3
Best Response
You've already chosen the best response.
4
lols , probably getting annoyed of me not getting it xD
myininaya
Best Response
You've already chosen the best response.
1
no its just late here
i been up for along time today
myininaya
Best Response
You've already chosen the best response.
1
a long*
polpak
Best Response
You've already chosen the best response.
0
Ditto!
myininaya
Best Response
You've already chosen the best response.
1
so what are the constants on both sides?
myininaya
Best Response
You've already chosen the best response.
1
the terms that don't have a x in them
Mimi_x3
Best Response
You've already chosen the best response.
4
ok , so x= a^3
Mimi_x3
Best Response
You've already chosen the best response.
4
t
Mimi_x3
Best Response
You've already chosen the best response.
4
ok , so x= a^3
myininaya
Best Response
You've already chosen the best response.
1
t and what is it on the other side?
myininaya
Best Response
You've already chosen the best response.
1
remember you are looking for non-x terms
Mimi_x3
Best Response
You've already chosen the best response.
4
ok , so x= a^3
Mimi_x3
Best Response
You've already chosen the best response.
4
a
myininaya
Best Response
You've already chosen the best response.
1
a or a^2?
Mimi_x3
Best Response
You've already chosen the best response.
4
a
myininaya
Best Response
You've already chosen the best response.
1
\[P(x)=x^3-a^2x-x^2+a^2=x^3+rsx^2+sx+t \]
^ ^
| |
a^2 = t
Mimi_x3
Best Response
You've already chosen the best response.
4
a^2 my bad
myininaya
Best Response
You've already chosen the best response.
1
so what is s again?
and what is t again?
Mimi_x3
Best Response
You've already chosen the best response.
4
s = 1
t = a^2
myininaya
Best Response
You've already chosen the best response.
1
s is not 1
Mimi_x3
Best Response
You've already chosen the best response.
4
a^3
myininaya
Best Response
You've already chosen the best response.
1
not a^3
scroll up
we have it above
Mimi_x3
Best Response
You've already chosen the best response.
4
-a^2
Mimi_x3
Best Response
You've already chosen the best response.
4
lolss , im so~ slow
myininaya
Best Response
You've already chosen the best response.
1
YES! :)
Mimi_x3
Best Response
You've already chosen the best response.
4
lols , finally i get it
myininaya
Best Response
You've already chosen the best response.
1
ok now s+t is -a^2+a^2 right?
Mimi_x3
Best Response
You've already chosen the best response.
4
yeah
myininaya
Best Response
You've already chosen the best response.
1
but what is -a^2+a^2?
Mimi_x3
Best Response
You've already chosen the best response.
4
so substitute it in s and t
Mimi_x3
Best Response
You've already chosen the best response.
4
idk
myininaya
Best Response
You've already chosen the best response.
1
-5+5 is
myininaya
Best Response
You've already chosen the best response.
1
-6+6 is
-24+24 is
-999+999 is
Mimi_x3
Best Response
You've already chosen the best response.
4
where did 5 come from ?
myininaya
Best Response
You've already chosen the best response.
1
i'm just trying to help you think what -a^2+a^2 is
Mimi_x3
Best Response
You've already chosen the best response.
4
0 ?
myininaya
Best Response
You've already chosen the best response.
1
yes! :)
myininaya
Best Response
You've already chosen the best response.
1
and now you are done
Mimi_x3
Best Response
You've already chosen the best response.
4
really ? omg ! yay i got it right xD
Mimi_x3
Best Response
You've already chosen the best response.
4
thank you very mcuh for helping (:
myininaya
Best Response
You've already chosen the best response.
1
np