Explanation

Let one of the roots of the given equation be ‘a’. Then, the other root will be ‘2a’.

∴ Sum of the roots = a + 2a = -(3k+4)/2

or, a = -(3k+4)/6 ----- (i)

∴ Product of the roots = a*2a = \(2a^2\)= \((9k^2-3k-1)/2\)

or, \(a^2\) = \((9k^2-3k-1)/4\) ---- (ii)

Combining (i) and (ii),

⇒ \(72k^2\)−51k−25 = 0

⇒(3k + 1)(24k − 25) = 0

Therefore, k = -1/3, 25/24.

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