Answer:
The product of the roots of a polynomial equation can be found by examining the coefficients of the equation. In the case of the equation x^3 - 4x^2 + x + 6 = 0, we can use Vieta's formulas to determine the product of the roots.
Vieta's formulas state that for a polynomial equation of the form ax^n + bx^(n-1) + cx^(n-2) + ... + k = 0, where a, b, c, ..., k are constants and n is the degree of the polynomial, the product of the roots is given by (-1)^n * (k/a).
In our equation x^3 - 4x^2 + x + 6 = 0, we have a = 1 and k = 6. The degree of the polynomial is n = 3. Plugging these values into Vieta's formulas, we get:
Product of roots = (-1)^3 * (6/1) = -6
Therefore, the product of the roots of the equation x^3 - 4x^2 + x + 6 = 0 is -6.
Explanation: