If the roots of an equation in x are 1, 2, 4:

(x - 1)(x - 2)(x - 4) = 0

=> (x^2 - x - 2x + 2)(x - 4) = 0

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

=> x^3 - 4x^2 - 3x^2 + 12x + 2x - 8 = 0

=> x^3 - 7x^2 + 14x - 8 = 0

**The required equation is x^3 - 7x^2 + 14x - 8 = 0**

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