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, $\displaystyle b^2-4ac < 0$

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

$\displaystyle 4k^2-16k < 0$

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

k < 0 or 4k < 16

k < 4

Range of Values of k is k < 4

ii) Stucked!