The values of k for which the roots are real and equal of the following equation $5x^2$ - 4x + 2 + k$(4x^2$ - 2x - 1) = 0 are $k = \dfrac{-6}{5}, 1$

Rewriting the equation gives (5 + 4k)x^2 + (-4 - 2k)x + (2 - k) = 0. Using the condition for equal roots, the discriminant b^2 - 4ac must equal zero: (-4 - 2k)^2 - 4(5 + 4k)(2 - k) = 0. Expanding yields 16 + 16k + 4k^2 - 4(10 - 3k - 4k^2) = 0, which simplifies to 20k^2 + 28k - 24 = 0. Solving this quadratic gives k = 3/5 and k = -2, which do not match the stated values; therefore, the statement is false.

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