The question is:

Given that the equation kx^2 - 4x + (k-3) = 0 has real roots, show that k^2 - 3k - 4 < 0.

Find the range of values of k satisfying this inequality.

b^2 - 4ac = 0

(-4)^2 - 4(k)(k-3) = 0

16 - 4k^2 + 12k = 0

(/4 4 - k^2 + 3k = 0

(Rearranged) k^2 - 3k - 4 = 0

(Factorized) (k-4)(k+1) = 0

k =4,-1I'm guessing that the rest involves the solution of an inequality but what would I do here?