Quick couple of question's I need some help on :)

[nina_rox]

Hey, could any help me with this questions... I feel so stupid asking this... but some reason it hasn't worked for me..

Show that the equation (k+1)x^2 - 2x - k = 0 has a solution for all values of k

[TrueTears]

hint: think about the quadratic formula and the determinant, b^2-4ac, now if b^2-4ac=>0 then there is at least one solution, so sub in the values for b, a, c (ax^2+bx+c) and show it is indeed =>0

[nina_rox]

Yeah I tried it but it doesn't seem to work...

[nina_rox]

Am I right saying that a=k+1 and b=-2 and c=-k? If so, it didn't work for me...

[Bhootnike]

Am I right saying that a=k+1 and b=-2 and c=-k? If so, it didn't work for me...

u sure this isnt complex numbers haha

[nina_rox]

mmm... am I not doing it right?

[trinh]

Show that the equation has a solution for all values of k

Therefore, must show that:

=>
                     

Now, if we treat the stuff inside the brackets, , as a function, say , we can see that it is always above the horizontal axis (k-axis)...

Therefore, for all real values of k; in fact, for all values of k

So going back to what we had to show; that is, that :

- We know that
- So what we have to show is the same as showing that

We know this is true from our earlier calculations, so we have thus showed that has a solution for all values of k

Sorry about the incoherent explanation ><

[nina_rox]

Thanks Trinh, I got 4(k^2+k+1) but wasn't sure what to do from there but that makes sense. Thank you!