Discriminant of a function.

Question

Consider the function $f(x)=kx^{2}-2kx+2.$

Find the values of $k$ if $kx^{2}+2>2kx$ for any value of $x$.

I am unsure how to start off this question. I thought it involves the discriminant but couldn't figure out which condition to apply. Any help will be appreciated.

Answer 1

I'm not sure if this is right...

please comment if it is wrong

i) $k>0$

$kx^2-2kx+2>0$

$D=k^2-2k<0$

$0<k<2$

ii) $k=0$

$2>0$ -> True

iii) $k<0$

$kx^2-2kx+2>0$ -> cannot be always true

Therefore, $0\leq k<2$