1. ## Infinite Roots.

$\\ Consider the function f(x) = \sqrt{x+a \sqrt x + b} + \sqrt x -c for some real constants a,b,c. For what values of a,b,c does the function have infinitely many roots?$

2. ## Re: Infinite Roots.

where do you get all these questions from!? i want one

3. ## Re: Infinite Roots.

Originally Posted by barbernator
where do you get all these questions from!? i want one
Secretz

If you want one, try the one I gave above!

4. ## Re: Infinite Roots.

Originally Posted by Fus Ro Dah
carrot

If you want one, try the one I gave above!
sounds right!

5. ## Re: Infinite Roots.

abc,4,4,2. there may be others...

6. ## Re: Infinite Roots.

Originally Posted by dd24
was expecting tips on how to sex infinite
strong english/10

7. ## Re: Infinite Roots.

Originally Posted by barbernator
abc,4,4,2. there may be others...
Yep there are more... in fact it's an inequality.

8. ## Re: Infinite Roots.

my sol isnt an inequality, but when b=a^2/4 and when c=a/2, the function will have infinite roots.

therefore, for b>0, all real a, and all real c, the function CAN have unlimited roots. again, no idea if it is correct.

9. ## Re: Infinite Roots.

btw fus, what is the actual answer to this?

10. ## Re: Infinite Roots.

c > 0 and a = -2c and b = c.

11. ## Re: Infinite Roots.

Originally Posted by barbernator
btw fus, what is the actual answer to this?
This.

Originally Posted by Carrotsticks
c > 0 and a = -2c and b = c.

12. ## Re: Infinite Roots.

What the fuck? How the fuck do you do this?

13. ## Re: Infinite Roots.

Originally Posted by someth1ng
What the fuck? How the fuck do you do this?
Think... what types of functions have infinite roots?

14. ## Re: Infinite Roots.

Originally Posted by Carrotsticks
Think... what types of functions have infinite roots?
I swear I havent encountered infinite roots...or sinx? cosx?

15. ## Re: Infinite Roots.

oh shit i see now lol. Just make the brackets a pertect square and factorise to cancel to 0

16. ## Re: Infinite Roots.

Originally Posted by someth1ng
I swear I havent encountered infinite roots...or sinx? cosx?
Indeed periodic functions like those (not all though of course). Any others?

17. ## Re: Infinite Roots.

y=0 for infinite roots...RIGHT!

18. ## Re: Infinite Roots.

when i did it originally, i differentiated and found the values of a and b when to make the derivative have a value of 0. and then i subbed into the initial function to find c. why did this not work?

19. ## Re: Infinite Roots.

Originally Posted by barbernator
when i did it originally, i differentiated and found the values of a and b when to make the derivative have a value of 0. and then i subbed into the initial function to find c. why did this not work?
Isn't that assuming the root is at a SP?

20. ## Re: Infinite Roots.

Originally Posted by Bored_of_HSC
Isn't that assuming the root is at a SP?
the x values cancelled, so there were no variable terms. So I just had a relation between a and b....

NVM fml, I neglected the denominator fack!

21. ## Re: Infinite Roots.

Originally Posted by barbernator
the x values cancelled, so there were no variable terms. So I just had a relation between a and b....

NVM fml, I neglected the denominator fack!
Ahhh. I should stop trying to do questions in my head lol.

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