Final answer:
To solve the polynomial function f(x) = x³+4x²+x-6, you can apply techniques like factoring, synthetic division, or the rational root theorem to find its roots.
Step-by-step explanation:
To solve the polynomial function f(x) = x³+4x²+x-6, we set the equation equal to zero: x³+4x²+x-6 = 0. There is no specific method to solve this equation, but we can apply different techniques like factoring, synthetic division, or using the rational root theorem to find its roots.
After solving, we find that the roots of the equation are x = -3, x = 1, and x ≈ 1.675. Therefore, the solutions to the polynomial function f(x) = x³+4x²+x-6 are x = -3, x = 1, and x ≈ 1.675.