Find the value of k so that the sum of the roots of kx^2–2kx–6x–6=0 is 4. After determining k, find out the roots of the resulting equation.

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The sum of the roots of kx^2–2kx–6x–6=0 has to equal 4.

kx^2–2kx–6x–6=0

kx^2 + x(-2k - 6) - 6 = 0

The sum of the roots is (2k - 6)/k

(2k - 6)/k = 4

=> 2k - 6 = 4k

=> k = -3

The equation is 3x^2 - 12x + 6 = 0

=> x^2 - 4x + 3 = 0

=> x^2 - 3x - x + 3 = 0

=> x(x - 3) - 1(x - 3) = 0

=> (x - 1)(x - 3) = 0

The roots are x = 1 and x = 3.

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