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Mathematics 14 Online
OpenStudy (anonymous):

pleaze help me!!! I need two numbers that can be multiplied and = -20 but when you add the two numbers they have to = -5

OpenStudy (anonymous):

it's impossble to be like that show me the function that u stuck with

OpenStudy (anonymous):

a^2 – 5a – 20 here is the problem

OpenStudy (zzr0ck3r):

a+b = -5 a*b = -20 a = -20/b -20/b+b=-5 -20+b^2 = -5b when b!=0 b^2 +5b-20 = 0 b = -(sqrt(105)+5)/2 or b = (sqrt(105)-5)/2 so a = -20(2/(sqrt(105)-5))

OpenStudy (zzr0ck3r):

or a = -20(-2/(sqrt(105)+5))

OpenStudy (anonymous):

????????????????

OpenStudy (anonymous):

-20+b^2 = -5b when b!=0(where did u get that )

OpenStudy (anonymous):

its suppose to look like (x+5)(x+9)

OpenStudy (anonymous):

my homework

OpenStudy (zzr0ck3r):

-20/b+b=-5 (-20+b^2)/b = -5 -20+b^2 = -5b as long as b!=0

OpenStudy (zzr0ck3r):

@savannajadey what part do you not get?

OpenStudy (phi):

Are you supposed to factor a^2 – 5a – 20 This does not factor into nice numbers or solve a^2 – 5a – 20=0 if this is the problem, you use the "quadratic formula"

OpenStudy (anonymous):

how u wrote it

OpenStudy (zzr0ck3r):

I had to complete the square for the quadratic, but I did not show all that as it would have looked ugly

OpenStudy (zzr0ck3r):

it is not -5a its +5a

OpenStudy (anonymous):

no its not @phi

OpenStudy (anonymous):

no its a -

OpenStudy (zzr0ck3r):

first i used a*b = -20 to write a in terms of b. then I plugged in for a and solved the quadratic equation. the i used my information of b to solve for a. the two sets of numbers do in fact add to -5 and multiply to -20

OpenStudy (zzr0ck3r):

a+b = -5 a*b= -20 solve for a in eq 2 a = -20/b no plug this into equation 1 -20/b+b = -5 now find comon denom (-20+b^2)/b= -5 multiply both sides by b -20+b^2 = -5b so now we have b^2-5b-20 = 0 or we could write this as -b^2+5b+20 = 0

OpenStudy (zzr0ck3r):

are you with me so far?

OpenStudy (anonymous):

i need two numbers thats it

OpenStudy (anonymous):

when u multiply then it has to = -20 and when u add them they have to = -5

OpenStudy (zzr0ck3r):

a = (sqrt(105)-5)/2 b = -40/(sqrt(105)-5)

OpenStudy (zzr0ck3r):

a+b = -5 and a*b = -20

OpenStudy (zzr0ck3r):

those are two such numbers...there are two more....

OpenStudy (phi):

here are your choices 1,20 2,10 4,5 if you assign opposite signs (to get -20) you have -1+20 = 19 1 -20= -19 -2+10= +8 2-10= -8 -4+5= 1 4-5=-1 there is no -5. uh oh..

OpenStudy (zzr0ck3r):

@phi why are those the only two choices? what is wrong with my two numbers?

OpenStudy (anonymous):

nevermind

OpenStudy (phi):

There is a solution, but it involves square roots...

OpenStudy (zzr0ck3r):

savanna take the two numbers i gave you. add them together and you get -5 multiply them together and you get -20

OpenStudy (zzr0ck3r):

did anyone say we can use square roots?

OpenStudy (zzr0ck3r):

there are two sets of solutions....both involve square roots

OpenStudy (phi):

It would help to know exactly what the question is/was.

OpenStudy (zzr0ck3r):

I have solved this twice, if you have any questions feel free to ask...

OpenStudy (zzr0ck3r):

well it says two numbers. it does not say integers or natural numbers so i assume real.

OpenStudy (zzr0ck3r):

as we only work with real numbers when at this level(for the most part)

OpenStudy (anonymous):

i get it @savannajadey

OpenStudy (zzr0ck3r):

lol, what did I do that we dont get?

OpenStudy (zzr0ck3r):

@savannajadey do you understand how I got to the quadratic?

OpenStudy (anonymous):

nope

OpenStudy (anonymous):

a^2-5a-20=0 a^2-5a-14(-6)=0 (a-7)(a+2)-6=0

OpenStudy (anonymous):

how is sound

OpenStudy (anonymous):

but when u multiply then it doesnt = -20

OpenStudy (anonymous):

yeah but first i did the simplifying

OpenStudy (anonymous):

ok

OpenStudy (anonymous):

-14-6=-20

OpenStudy (zzr0ck3r):

when you multiply the two numbers I gave it does = -20

OpenStudy (anonymous):

dn't forget best answer plz

OpenStudy (anonymous):

what are the two number

OpenStudy (anonymous):

it's 7 and 2

OpenStudy (anonymous):

-7 and +2

OpenStudy (zzr0ck3r):

-7*2 != -20

OpenStudy (anonymous):

but thoose multiplied dont = -20

OpenStudy (anonymous):

yeah but we add to the function (-6)

OpenStudy (zzr0ck3r):

the two numbers are -40/(sqrt(105)-5) and (sqrt(105)-5)/2 twy it out.... there is not two such integers, and I can show a proof for that...

OpenStudy (anonymous):

u can only hav two number @moha_10

OpenStudy (zzr0ck3r):

moha_10 we cant make a function we already have the two relations a+b = -5 and a*b=-20 we cant change the two relations

OpenStudy (anonymous):

okay i did it two number

OpenStudy (anonymous):

there just simply # like 5 and -6

OpenStudy (zzr0ck3r):

ok @savannajadey a+b = -5 a*b= -20 solve for a in eq 2 a = -20/b no plug this into equation 1 -20/b+b = -5 now find comon denom (-20+b^2)/b= -5 multiply both sides by b -20+b^2 = -5b so now we have b^2-5b-20 = 0 or we could write this as -b^2+5b+20 = 0 tell me what part of this you dont get.

OpenStudy (anonymous):

@zzr0ck3r all has his or her way

OpenStudy (zzr0ck3r):

there are no such "simple" numbers.

OpenStudy (zzr0ck3r):

what @moha_10 ?

OpenStudy (anonymous):

@zzr0ck3r what are the two numbers u said it was

OpenStudy (zzr0ck3r):

-40/(sqrt(105)-5) and (sqrt(105)-5)/2

OpenStudy (anonymous):

ya @zzr0ck3r ive done this lession for the last hr now

OpenStudy (anonymous):

alright but the number that i added to it's not realated to two numbers

OpenStudy (anonymous):

nevermind ill figure it by myself

OpenStudy (zzr0ck3r):

@savannajadey tell me what you dont understnad from that I just posted and we can go from there. If you check those numbers they work and I can show you how to get there. but stay with me and stop with the attempts at a natural or integer. there is no such numbers.

OpenStudy (zzr0ck3r):

the two numbers I gave you will work and there are two more, that is all, there are no other numbers that will work.

OpenStudy (anonymous):

yes there is im doing factoring trianomials and there are only two numbers

OpenStudy (zzr0ck3r):

?

OpenStudy (anonymous):

?

OpenStudy (zzr0ck3r):

if you look at what I showed you can see that there are no such "simple" numbers...I dont understand what you are saying that because your doing trinomial factoring there must be two such numbers?

OpenStudy (anonymous):

nmnm nm nm nm

OpenStudy (zzr0ck3r):

ok but do you see that the two numbers I gave you do in fact add to -5 and multiply to -20?

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