What are the values of k for which the polynomial (k-3)x^{2}-kx-1 has <strong>NO</strong> real linear factors?

Explanation

For the quadratic polynomial to have no real linear factors, its discriminant must be less than zero. D = (-k)^2 - 4(k-3)(-1) = k^2 + 4k - 12 \lt 0. Factoring yields (k+6)(k-2) \lt 0, which gives -6 \lt k \lt 2.

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