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The cubic equation with roots -2, -1, and 1 has coefficients 1, 2, -3, and -2.

To find the coefficients of a cubic equation with roots r1, r2, and r3, we can use the fact that the equation can be written in the form:

(x - r1)(x - r2)(x - r3) = 0

Expanding this expression gives:

x^3 - (r1 + r2 + r3)x^2 + (r1r2 + r1r3 + r2r3)x - r1r2r3 = 0

Therefore, the coefficients of the cubic equation are:

- the coefficient of x^3 is 1

- the coefficient of x^2 is -(r1 + r2 + r3) = -(-2 - 1 + 1) = 2

- the coefficient of x is r1r2 + r1r3 + r2r3 = (-2)(-1) + (-2)(1) + (-1)(1) = -3

- the constant term is -r1r2r3 = -(-2)(-1)(1) = -2

Hence, the cubic equation with roots -2, -1, and 1 is:

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

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