Challenge for 2u peeps (3 Viewers)

[HeroicPandas]

I never learnt that. What r u on about. isnt that 3u?

It's my favourite topic in 2U!

http://www.boredofstudies.org/courses/maths/2u/1119956014_2004_Mathematics_Notes_Emily_Meers.pdf

 

[fishrushed]

Can't seem to get the answer by itself. I keep getting an extra bit on top of what I have to show (k< -25)
Must be bad news for me

 

[fishrushed]

I never learnt that. What r u on about. isnt that 3u?

It's a 2U topic. There is quadratic formula and discriminant, sum and product of roots and some other things in that topic.

 

[Sy123]

Can't seem to get the answer by itself. I keep getting an extra bit on top of what I have to show (k< -25)
Must be bad news for me

The only thing you need to actually show is that k > 1.

The upper bound ( k < 25/24) comes much more simply than you might think.

 

[darlking]

Oh ok, well that was last year and don't expect me to remember my topic names last year.

 

[darlking]

The only thing you need to actually show is that k > 1.

How do you show k >1 when you can also show k < 25/24. I found the 25/24 one.

 

[Sy123]

How do you show k >1 when you can also show k < 25/24. I found the 25/24 one.

By using the quadratic formula, we can find that:





What do we get when alpha - beta?

We get an inequality in terms of k.

What is the solution to this inequality?
One of them is k > 1.

 

[superSAIyan2]

Too get the other inequality use discriminant properties and your knowledge of real and unreal roots (i.e. what is the definite condition for there to be real roots)

 

[omgiloverice]

thank god, nobody solved it before I got back from my 7hr tutor -.-

 

[Trebla]

By using the quadratic formula, we can find that:





What do we get when alpha - beta?

We get an inequality in terms of k.

What is the solution to this inequality?
One of them is k > 1.

Umm...doesn't that lead an inequality with an unknown in the denominator which is beyond the 2u course?

This is what I get without requiring an unknown in the denominator.

Suppose that and are the roots where . We are given that

Sum of roots:



Product of roots:



But



Since



then



Substituting the result we get



Note that since the denominator is always non-negative, the sign of the inequality is unchanged (whereas in your case you need to deal with cases where k is positive/negative etc).

Looking at the left inequality we immediately get the upper bound.



Looking at the right inequality.



Tehnically speaking, putting the inequalities together we should get



Missing a solution set haya!

 

[darlking]

tHANk you Trebla!

 

[hayabusaboston]

thank god, nobody solved it before I got back from my 7hr tutor -.-
View attachment 28102

Actually heroicpandas did b4 anyone LOL he just didnt post it here.

 

[omgiloverice]

Actually heroicpandas did b4 anyone LOL he just didnt post it here.

ahh crap i forgot about that... well I am the first person who doesn't do 4U to solve it

 

[HeroicPandas]

ahh crap i forgot about that... well I am the first person who doesn't do 4U to solve it

Very nice!

"Now we can sacrifice the k inequalities..."

i like this

 

[fishrushed]

The only thing you need to actually show is that k > 1.

The upper bound ( k < 25/24) comes much more simply than you might think.

yea, I got k< 25/24 and k>1, but I happened to also have gotten k<-25 along with the k>1 and I just stopped there

 

[fishrushed]

Tehnically speaking, putting the inequalities together we should get



Missing a solution set haya!

Oh good at least the k<-25 i found wasn't a dud solution

 

[hayabusaboston]

Umm...doesn't that lead an inequality with an unknown in the denominator which is beyond the 2u course?

This is what I get without requiring an unknown in the denominator.

Suppose that and are the roots where . We are given that

Sum of roots:



Product of roots:



But



Since



then



Substituting the result we get



Note that since the denominator is always non-negative, the sign of the inequality is unchanged (whereas in your case you need to deal with cases where k is positive/negative etc).

Looking at the left inequality we immediately get the upper bound.



Looking at the right inequality.



Tehnically speaking, putting the inequalities together we should get



Missing a solution set haya!

Well thats certainly the most cheerie way anyone has addressed me in the past few days LOL
Indeed.
Well the intention was to make it neat, so I just left that extra one out in the question.

 

[hayabusaboston]

ahh crap i forgot about that... well I am the first person who doesn't do 4U to solve it

Oh and

omgilovericetoo

 

[Amiiiiiin]

I found that k > 1 by finding K. but i cant get the relation between k 25/24

 

[hayabusaboston]

I found that k > 1 by finding K. but i cant get the relation between k 25/24

Use discriminant and sum and product of roots.