For what real values of k will the roots of the equation kx^2-3kx=2 be real numbers?

Answer 1

k x^2 -3k x - 2 = 0

a = k
b = -3k
c = -2
look at b^2 - 4 a c

look at parabola y = 9k^2 + 8 k
must be 0 or +
for 0
k (9k+8) = 0
k = 0 or k= -8/9
between them, y is negative
SO
k</= -8/9
or
k>/=0