Typenick a dit :

Lemme mess with you a little, can I? :D
I've solved both of those exercises some time ago, but I haven't got the chance to check if I did them right yet.

1. Given is an equation with variable x:


For which values of alpha has this equation 2 real different roots with the same signs?

Edit: made a mistake in 1, sorry

Worsnoplover a dit :

Yeah, I think I read it with '' different signs'' at first, which would be impossible.
Anyways, giving a thought on this.
In order to have 2 different roots:
=> D > 0
=> D= b^2 - 4ac = 8cos^2alpha - 4(cosalpha + 1)
=> 8cos^2alpha - 4(cosalpha + 1) > 0

In order for the roots to have same signs:
=> c/a > 0
=> 1/ (cosalpha+1) > 0
=> cosalpha + 1 > 0
=> cosalpha > -1

You put 8cos^2alpha - 4(cosalpha+1) > 0 and cosalpha > -1 in a system, solve each of them and find the solution.
Cba to solve it atm lol, I hope you can continue it. If not, tell me so I could go til the end.

PS: Not dealing with the 2nd as I don't quite get the exercise since am not used to maths in english, sorry.

Worsnoplover a dit :

Anyways, giving a thought on this.

Nikol a dit :

I am scared to grow up now.

Typenick a dit :

Your solution is fine and it's very similar to what I did. I was just wondering if I've got the result right (I've got 2pi/3 to pi, by the way).

2nd exercise is a bit more interesting. I've translated the thing from polish so feel free to point out if something's unclear or hard to understand.


Both of my exercises are taken from polish matura exam taken at age 19. This one comes from 1970, I believe.

Anyway, don't worry. It gets even worse later ;)

Typenick a dit :

2. Given is a set of triangles with common vertex in A=(0,6). Sides of those triangles opposite to the vertex A are contained in a straight line described by an equation: y + 2 = 0 and each of them has length of 4. Find equation of a curve that contains centers of circles described on those triangles.

Abdeltif a dit :

Help me get the short form of this please :(
2x(-4y+1)-(4x-xy)(4x+xy)+(y+2y)

God thanks that this thread is allowed <3

Foxyfoxfox a dit :

I don't think you can combince variables, it seems like you just have to simplify it..

Taeyeonrawr a dit :

2x(-4y+1)-(4x-xy)(4x+xy)+(y+2y)
-8xy+2x-16x^2+x^2y^2+y+2y
-8xy+2x-16x^2+x^2y^2+3y &lt;answer
because other 'members' aren't the same as the others

Abdeltif a dit :

Help me get the short form of this please :(
2x(-4y+1)-(4x-xy)(4x+xy)+(y+2y)

God thanks that this thread is allowed &amp;amp;lt;3

Koopafan a dit :

I'm willing to do anything 7/8th grade math or lower, (I'm in Algebra WOO) so I can do CLT (Combine Like Terms), Solving a System of Equations, Substitution, Elimination, etc.

Abcnicoles a dit :

I need help.


Identify the adjective phrase or the adverb phrase and prepositional phrase.
1. Years later, she gained fame as a world-class athlete.
2.all of her hard work made her strong
3.illnesses like these were often deadly
4.rudolph suffered from polio and scarlet fever when she was four years old.
5.for many years rudolph used a leg brace when she walked
Thx!