Questions: The solution set of the equation (x^4-5 x^3-30 x^2-40 x-16=0) is B. (Simplify your answers. Type exact answers, using radicals as needed. Use a comma to separate your answers as needed.)

Solution Steps

To solve the polynomial equation \(x^{4} - 5x^{3} - 30x^{2} - 40x - 16 = 0\), we can use numerical methods or symbolic computation to find the roots. Since this is a quartic equation, it may have up to four real or complex roots. We can use Python's libraries to find these roots, which may include real and complex numbers.

We are given the polynomial equation: \[ x^4 - 5x^3 - 30x^2 - 40x - 16 = 0 \]

The roots of the polynomial equation are found to be: \[ x = -2, \, x = -1, \, x = 4 - 2\sqrt{6}, \, x = 4 + 2\sqrt{6} \]

The roots are already in their simplest form, with two real roots and two roots expressed in terms of radicals.

Final Answer