Determine the coefficients of the quadratic equation with roots 2 and -3.

The quadratic equation with roots 2 and -3 has coefficients of 1, -(-2+(-3)), and 2*(-3) which simplifies to 1, 5, and -6.

To determine the coefficients of a quadratic equation with given roots, we can use the fact that the equation can be written in the form (x - r1)(x - r2) = 0, where r1 and r2 are the roots. Expanding this expression gives us x^2 - (r1 + r2)x + r1r2 = 0, which is the standard form of a quadratic equation.

In this case, the roots are 2 and -3, so we have (x - 2)(x + 3) = 0. Expanding this expression gives us x^2 + x - 6 = 0, which is the quadratic equation with the given roots.

Comparing this equation to the standard form, we can see that the coefficients are 1, -(-2+(-3)), and 2*(-3), which simplifies to 1, 5, and -6. Therefore, the quadratic equation with roots 2 and -3 has coefficients of 1, 5, and -6.