Discriminant and nature of roots

[momoko]

What is the least value of k if the roots of the equation x^2 - 2kx + k^2 = 3 + x are real?

These are the steps I have taken:
x^2 - 2kx + k^2 = 3 + x
x^2 - 2kx + k^2 - 3 -x = 0
x^2 - (2k - 1)x +k^2 - 3 = 0
since the discriminant b^2 - 4ac ? 0,
(2k - 1)^2 - 4x^2(k^2 - 3) ?0
4k^2 - 4k +1 - 4k^2x^2 + 12x^2 ? 0
4k^2 - 4k +1 - x^2(4k^2 + 12) ? 0
4k^2 - 4k +1 ? x^2(4k^2 + 12)
k^2 - k + 1/4 ? x^2(k^2 + 3)

then I am stuck from this step. what is wrong with this method?
the final solution should be -13/4

thank you in advance!

 

[Aladdin]

What is the least value of k if the roots of the equation x^2 - 2kx + k^2 = 3 + x are real?

These are the steps I have taken:
x^2 - 2kx + k^2 = 3 + x
x^2 - 2kx + k^2 - 3 -x = 0
x^2 - (2k - 1)x +k^2 - 3 = 0
since the discriminant b^2 - 4ac ? 0,
(2k - 1)^2 - 4x^2(k^2 - 3) ?0-----> What's this ! This is not a . . .

thank you in advance!

 

[Denis]

Discriminant is (-2k - 1)^2 - 4(k^2 - 3)
If you can't follow that, see your teacher...

 

[garf]

you can obtain the value of k, for the roots of the equation, if you group the coefficients of each power of " x" , and you obtain the value of a, b, c, and makes b[sup:uey7wncp]2[/sup:uey7wncp] -4ac> 0

 

[momoko]

thank you everyone, I understand how to solve it now
sorry for the late reply though.