Determine the coefficients of the quadratic equation with roots -4 and -1.

The quadratic equation with roots -4 and -1 has coefficients of 1, 5, and 4.

To determine the coefficients of the quadratic equation with roots -4 and -1, 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. Substituting -4 and -1 for r1 and r2, respectively, we get:

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

Expanding the brackets, we get:

x^2 + 5x + 4 = 0

Therefore, the coefficients of the quadratic equation with roots -4 and -1 are 1, 5, and 4. The coefficient of x^2 is always 1 in a quadratic equation of this form, and the other coefficients can be found by looking at the terms in the expanded equation. The coefficient of x is the sum of the roots (in this case, -4 and -1), and the constant term is the product of the roots (which is -4 times -1, or 4).