Question

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

Answer 1

is the polynomial written correctly?

Answer 2

woops my bad sorry
P(x) = x^3 +rx^2 +sx +t

Answer 3

Colorful pi can you help me?

Answer 4

let me try to help him and then i will look at your question

Answer 5

him ? are yu referring to me ?

Answer 6

is this algebra?

Answer 7

noo , its a polynomial question

Answer 8

so what class is it then?

Answer 9

class ? what do yu mean ? Its from the topic polynomials

Answer 10

\[P(x)=(x-1)(x-a)(x+a)=x^3+rs^2+sx+t\]

Answer 11

is that the answer ?

Answer 12

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

Answer 13

no , im not doing it for fun , its my maths assignment LOL

Answer 14

\[P(x)=x(x^2-a^2)-1(x^2-a^2)=x^3+rsx^2+sx+t\]

Answer 15

so the class is called polynomials lol?

Answer 16

what does yu mean by class ?

Answer 17

\[P(x)=x^3-a^2x-x^2+a^2=x^3+rsx^2+sx+t\]
people go to class to learn and get assignments lol

Answer 18

no the class is called maths LOL

Answer 19

\[P(x)=x^3-x^2-a^2x+a^2=x^3+rsx^2+sx+t\]

Answer 20

2 unit maths to be specific

Answer 21

ok we are almost done with this problem
can you guess what to do next?

Answer 22

we want both sides to be the same

Answer 23

collecting like terms ?

Answer 24

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?

Answer 25

they must be equal

Answer 26

so we need that for the other terms as well

Answer 27

we have
-1=rs
-a^2=s
a^2=t

Answer 28

I seriously think I'm being trolled here.. but just to ease my tired brain..

\[\sqrt{25} \ne -5\]

Answer 29

you are right polpak

Answer 30

wait , dnt yu factorise it further to (x^2-a^2)(x-1)

Answer 31

that =5

Answer 32

factor?

Answer 33

Someone was trying to tell me that it equals both 5 and -5

Answer 34

ok the objective is to find s+t

Answer 35

But I can only really prove it by going to the definition. Which they don't accept.

Answer 36

ohh yeah , my bad

Answer 37

Sorry for bothering you mimi, but myin rarely watches group chat (with good reason)

Answer 38

what do you think s+t is based on what i gave you above?
hint we don't need that first equation rs=-1

Answer 39

yu talking to me or polpak ? LOL

Answer 40

you

Answer 41

lols , tbh im lost , i dont get it xDD

Answer 42

do you understand when I wrote P
as P(x)=(x-1)(x-a)(x+a)?

Answer 43

yeah , i dont understand the part
-1 = rs
-a^2 = s
a^2 = t
where did yu get it from ?

Answer 44

both sides had to be equal we were looking at
\[P(x)=x^3-a^2x-x^2+a^2=x^3+rsx^2+sx+t \]

Answer 45

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

Answer 46

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?

Answer 47

ohh i get it
rs = -1

Answer 48

yes
now
what is the coefficient of x on the left hand side?
what is the coefficient of x on the right hand side?

Answer 49

x on the left hand side: 1 i think
x on the right hand side 1 i think

Answer 50

no what is the number in front of x on boths?

Answer 51

both sides*

Answer 52

there's no other number

Answer 53

-a^2?
s?

Answer 54

lols , its a letter not a number

Answer 55

they are numbers

Answer 56

they are ? arent they are called pronumerals ?

Answer 57

are they*

Answer 58

never heard of this term

Answer 59

ohh ok

Answer 60

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

Answer 61

becauce a and i can be words

Answer 62

ohh ok , i never knew that they are numbers xD

Answer 63

but usually the book will make it clear to you what they are

Answer 64

yep

Answer 65

ok , so x= a^3

Answer 66

a^3 is nowhere to be found
we aren;t solving equation for x

Answer 67

ok , so x= a^3

Answer 68

ohh ok

Answer 69

ok so look again at the polynomial
what is the coefficent of x on both sides?

Answer 70

ok , so x= a^3

Answer 71

ok , so x= a^3

Answer 72

x= s

Answer 73

ok no
\[P(x)=x^3-a^2x-x^2+a^2=x^3+rsx^2+sx+t \]
^ ^
| |

-a^2 = s

Answer 74

ok , so x= a^3

Answer 75

ohh lols , sorry im so slow of understanding it

Answer 76

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

Answer 77

god my english is getting bad

Answer 78

ok , so x= a^3

Answer 79

lols , probably getting annoyed of me not getting it xD

Answer 80

no its just late here
i been up for along time today

Answer 81

a long*

Answer 82

Ditto!

Answer 83

so what are the constants on both sides?

Answer 84

the terms that don't have a x in them

Answer 85

ok , so x= a^3

Answer 86

t

Answer 87

ok , so x= a^3

Answer 88

t and what is it on the other side?

Answer 89

remember you are looking for non-x terms

Answer 90

ok , so x= a^3

Answer 91

a

Answer 92

a or a^2?

Answer 93

a

Answer 94

\[P(x)=x^3-a^2x-x^2+a^2=x^3+rsx^2+sx+t \]
^ ^
| |
a^2 = t

Answer 95

a^2 my bad

Answer 96

so what is s again?
and what is t again?

Answer 97

s = 1
t = a^2

Answer 98

s is not 1