Determine the coefficients of the quadratic equation with roots -1 and 2.

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

To find the quadratic equation with roots -1 and 2, we start with the fact that a quadratic equation can be written in the form ax^2 + bx + c = 0, where a, b, and c are constants. We know that the roots of the equation are -1 and 2, so we can write the equation in factored form as (x + 1)(x - 2) = 0.

Expanding this expression gives us x^2 - x - 2 = 0, which is the quadratic equation we were looking for. Comparing this equation to the general form ax^2 + bx + c = 0, we can see that a = 1, b = -1, and c = -2. Therefore, the coefficients of the quadratic equation with roots -1 and 2 are 1, -1, and -2.

We can also check our answer by using the quadratic formula, which gives us x = (-b ± sqrt(b^2 - 4ac)) / 2a. Plugging in the values of a, b, and c that we found earlier, we get x = (1 ± sqrt(1 + 8)) / 2 and simplify to get x = -1 and x = 2, which are indeed the roots we were given.