Question

find the range of values of k if the equation (2-3k)x2 + (4-k)x+2=0 has two different roots

Answer 1

(2-3k)x^2 + (4-k)x+2=0
delta = (4-k)^2 - 8(2-3k) > 0
= k^2 - 8k + 16 - 16 + 24k >0
= k^2 + 16k >0
= k ( k + 16) >0
Thus k < 0 or k > 16

Answer 2

Given k ( k + 16) >0, what about the case where k< 0 AND (k + 16) <0?

Answer 3

k<-16 or k>0