for what value of k will the function

Question

f(x)=kx^2-4k+k have no zeros

Answer 1

No zeros means that the discriminant is negative

for f(x) = ax^2 + bx + c, the discriminant is b^2 - 4ac

So, we need

4^2 - 4k*k = 16 - 4k^2 = 4(4-k^2) < 0

So, as long as k^2 > 4, there will be no roots.