Discriminant of Roots - Stucked @ part ii after completing part i

I don't know how to do the part ii.

The equation of a curve is $\displaystyle y = 4x^2 - 2kx + k$

i) Find the range of values of k if the curve does not meet the x-axis.

ii) Show that the line $\displaystyle y = x + 1$ intersects the curve for all real values of k.

**Solution**

**i) Since curve does not meet x-axis, $\displaystyle b^2-4ac < 0$**

$\displaystyle -2k^2-4(4)(k) < 0$

$\displaystyle

-4k^2-16k < 0$

$\displaystyle k(-4k-16) < 0$

$\displaystyle

k < 0$ or $\displaystyle -4k < 16

k < -4$

Range of Values of $\displaystyle k$ is $\displaystyle k < -4$

**ii) Stucked!**