Mimi_x3
  • 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
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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myininaya
  • myininaya
is the polynomial written correctly?
Mimi_x3
  • Mimi_x3
woops my bad sorry P(x) = x^3 +rx^2 +sx +t
helpme1234
  • helpme1234
Colorful pi can you help me?

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

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